Code details
best found code with parameters
q=19 k=3 n=31
minimum distance = 28
this is new optimal code
the previous bounds were -1/28
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 75 orbits of sizes:
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6
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6
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2
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6
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6
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6
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3
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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3
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6
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6
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6
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6
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6
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2
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6
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6
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6
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6
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6
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1
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3
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6
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6
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6
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6
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3
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6
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2
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6
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6
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6
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6
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6
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6
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2
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6
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6
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6
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6
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6
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6
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6
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6
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6
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3
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6
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6
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6
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6
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6
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2
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2
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3
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6
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6
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2
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1
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1
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2
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2
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The solution of the corresponding linear system of equations was found after less than 100 seconds:
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0
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0
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0
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0
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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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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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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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0
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0
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0
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0
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0
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0
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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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0
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0
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0
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0
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0
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0
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0
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1
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0
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0
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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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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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2
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0
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2
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1
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1
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0
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0
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2
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3
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0
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3
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3
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0
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0
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0
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1
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3
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2
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3
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0
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0
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1
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2
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2
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3
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0
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3
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3
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2
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3
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3
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3
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3
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1
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2
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3
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3
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3
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1
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0
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1
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0
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2
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1
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3
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2
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3
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2
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2
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3
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3
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3
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3
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3
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3
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1
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2
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3
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1
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0
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1
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3
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0
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0
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0
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2
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0
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3
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0
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1
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1
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0
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3
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0
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1
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This produces the following generator matrix
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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0
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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18
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2
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16
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14
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8
|
12
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9
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2
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14
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12
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15
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4
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4
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4
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1
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16
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14
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17
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5
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11
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18
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1
|
3
|
3
|
3
|
15
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1
|
2
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16
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8
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8
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15
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0
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12
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15
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13
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18
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7
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18
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5
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7
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2
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1
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4
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11
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7
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18
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8
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4
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3
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13
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6
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1
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5
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11
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4
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11
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5
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13
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0
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1
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3
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8
|
Which is a code with the following weight distribution
1y31+2286x28y3+1512x29y2+1278x30y1+1782x31