Code details
best found code with parameters
q=23 k=3 n=484
minimum distance = 462
this is new optimal code
the previous bounds were -1/462
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 33 orbits of sizes:
3
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6
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4
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12
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12
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12
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12
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12
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12
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12
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12
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12
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12
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24
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24
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24
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24
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24
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24
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24
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24
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12
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24
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24
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24
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24
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12
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24
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24
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24
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12
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12
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12
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The solution of the corresponding linear system of equations was found after less than 100 seconds:
0
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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0
|
1
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1
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1
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1
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0
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1
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1
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1
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0
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0
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0
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0
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22
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21
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21
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21
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21
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21
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21
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21
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21
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21
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21
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22
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21
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21
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21
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22
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22
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22
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This produces the following generator matrix
22
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22
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22
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22
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22
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22
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11
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11
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22
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22
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2
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2
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9
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9
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20
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20
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13
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13
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11
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11
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22
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22
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16
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16
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6
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6
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17
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17
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5
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5
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11
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11
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22
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22
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4
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4
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18
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18
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7
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7
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15
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15
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11
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11
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22
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22
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1
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1
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10
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10
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21
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21
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12
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12
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11
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11
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22
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22
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4
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4
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18
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18
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7
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7
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15
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15
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11
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11
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22
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22
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19
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19
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3
|
3
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14
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14
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8
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8
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11
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11
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22
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22
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16
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16
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6
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6
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17
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17
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5
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5
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11
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11
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22
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22
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1
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1
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10
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10
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21
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21
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12
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12
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11
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11
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22
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22
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19
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19
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3
|
3
|
14
|
14
|
8
|
8
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11
|
11
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22
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22
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2
|
2
|
9
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9
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20
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20
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13
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13
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11
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11
|
2
|
2
|
16
|
16
|
19
|
19
|
6
|
6
|
3
|
3
|
9
|
9
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20
|
20
|
14
|
14
|
17
|
17
|
8
|
8
|
5
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5
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13
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13
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2
|
2
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2
|
2
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4
|
4
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18
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18
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9
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9
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9
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9
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20
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20
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20
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20
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7
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7
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15
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15
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13
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13
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13
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13
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2
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2
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1
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1
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1
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1
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10
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10
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10
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10
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9
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9
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20
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20
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21
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21
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21
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21
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12
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12
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12
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12
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13
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13
|
2
|
2
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16
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16
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4
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4
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18
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18
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6
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6
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9
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9
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20
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20
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17
|
17
|
7
|
7
|
15
|
15
|
5
|
5
|
13
|
13
|
2
|
2
|
16
|
16
|
19
|
19
|
6
|
6
|
3
|
3
|
9
|
9
|
20
|
20
|
14
|
14
|
17
|
17
|
8
|
8
|
5
|
5
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13
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13
|
2
|
2
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16
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16
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4
|
4
|
18
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18
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6
|
6
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9
|
9
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20
|
20
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17
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17
|
7
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7
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15
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15
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5
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5
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13
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13
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2
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2
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1
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1
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19
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19
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10
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10
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3
|
3
|
9
|
9
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20
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20
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14
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14
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21
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21
|
8
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8
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12
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12
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13
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13
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2
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2
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1
|
1
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19
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19
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10
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10
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3
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3
|
9
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9
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20
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20
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14
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14
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21
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21
|
8
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8
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12
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12
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13
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13
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16
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16
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4
|
4
|
1
|
1
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18
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18
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6
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6
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10
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10
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21
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21
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17
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17
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7
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7
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12
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12
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15
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15
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5
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5
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16
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16
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4
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4
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1
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1
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18
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18
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6
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6
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10
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10
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21
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21
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17
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17
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7
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7
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12
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12
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15
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15
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5
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5
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16
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16
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19
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19
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19
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19
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6
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6
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3
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3
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3
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3
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14
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14
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14
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14
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17
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17
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8
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8
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8
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8
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5
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5
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16
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16
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16
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16
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1
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1
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6
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6
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6
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6
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10
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10
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21
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21
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17
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17
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17
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17
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12
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12
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5
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5
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5
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5
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4
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4
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1
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1
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18
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18
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19
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19
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10
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10
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3
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3
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14
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14
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21
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21
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8
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8
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7
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7
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12
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12
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15
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15
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4
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4
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4
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4
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18
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18
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18
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18
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19
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19
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3
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3
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14
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14
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8
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8
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7
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7
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7
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7
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15
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15
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15
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15
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4
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4
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1
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1
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18
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18
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19
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19
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10
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10
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3
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3
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14
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14
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21
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21
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8
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8
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7
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7
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12
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12
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15
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15
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22
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11
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22
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11
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2
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13
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22
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11
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9
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20
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9
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20
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22
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11
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2
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13
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16
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5
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22
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11
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6
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17
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6
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17
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22
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11
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16
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5
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4
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15
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22
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11
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18
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7
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18
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7
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22
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11
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4
|
15
|
1
|
12
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22
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11
|
10
|
21
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10
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21
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22
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11
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1
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12
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18
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7
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4
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15
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22
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11
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22
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11
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4
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15
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18
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7
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19
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8
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22
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11
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3
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14
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3
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14
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22
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11
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19
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8
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6
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17
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16
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5
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22
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11
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22
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11
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16
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5
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6
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17
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10
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21
|
1
|
12
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22
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11
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22
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11
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1
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12
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10
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21
|
3
|
14
|
19
|
8
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22
|
11
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22
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11
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19
|
8
|
3
|
14
|
9
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20
|
2
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13
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22
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11
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22
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11
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2
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13
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9
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20
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16
|
5
|
2
|
13
|
6
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17
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19
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8
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9
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20
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3
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14
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3
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14
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9
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20
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19
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8
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6
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17
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2
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13
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16
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5
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4
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9
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20
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15
|
2
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13
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9
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20
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2
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18
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7
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13
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2
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18
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7
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13
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9
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20
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2
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13
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4
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9
|
20
|
15
|
1
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12
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2
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10
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21
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13
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1
|
9
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20
|
12
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10
|
21
|
10
|
21
|
1
|
9
|
20
|
12
|
2
|
10
|
21
|
13
|
1
|
12
|
18
|
7
|
9
|
20
|
6
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17
|
2
|
13
|
4
|
15
|
16
|
5
|
16
|
5
|
4
|
15
|
2
|
13
|
6
|
17
|
9
|
20
|
18
|
7
|
19
|
8
|
3
|
14
|
2
|
13
|
9
|
20
|
16
|
5
|
6
|
17
|
6
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17
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16
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5
|
9
|
20
|
2
|
13
|
3
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14
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19
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8
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6
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17
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18
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7
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9
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20
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16
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5
|
2
|
13
|
4
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15
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4
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15
|
2
|
13
|
16
|
5
|
9
|
20
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18
|
7
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6
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17
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10
|
21
|
3
|
14
|
9
|
20
|
2
|
13
|
1
|
12
|
19
|
8
|
19
|
8
|
1
|
12
|
2
|
13
|
9
|
20
|
3
|
14
|
10
|
21
|
3
|
14
|
9
|
20
|
10
|
21
|
19
|
8
|
2
|
13
|
1
|
12
|
1
|
12
|
2
|
13
|
19
|
8
|
10
|
21
|
9
|
20
|
3
|
14
|
4
|
15
|
16
|
5
|
18
|
7
|
1
|
12
|
10
|
21
|
6
|
17
|
6
|
17
|
10
|
21
|
1
|
12
|
18
|
7
|
16
|
5
|
4
|
15
|
1
|
12
|
10
|
21
|
16
|
5
|
6
|
17
|
18
|
7
|
4
|
15
|
4
|
15
|
18
|
7
|
6
|
17
|
16
|
5
|
10
|
21
|
1
|
12
|
19
|
8
|
16
|
3
|
14
|
5
|
3
|
14
|
19
|
6
|
17
|
8
|
19
|
6
|
17
|
8
|
3
|
14
|
16
|
3
|
14
|
5
|
19
|
8
|
6
|
10
|
21
|
17
|
6
|
17
|
16
|
1
|
12
|
5
|
16
|
5
|
16
|
5
|
16
|
1
|
12
|
5
|
6
|
17
|
6
|
10
|
21
|
17
|
1
|
12
|
4
|
15
|
19
|
8
|
18
|
7
|
3
|
14
|
10
|
21
|
10
|
21
|
3
|
14
|
18
|
7
|
19
|
8
|
4
|
15
|
1
|
12
|
18
|
19
|
8
|
7
|
4
|
3
|
14
|
15
|
4
|
15
|
18
|
7
|
18
|
7
|
4
|
15
|
4
|
3
|
14
|
15
|
18
|
19
|
8
|
7
|
3
|
14
|
19
|
8
|
10
|
21
|
1
|
12
|
18
|
7
|
4
|
15
|
4
|
15
|
18
|
7
|
1
|
12
|
10
|
21
|
19
|
8
|
3
|
14
|
Which is a code with the following weight distribution
1y484+1452x462y22+10648x463y21+66x484