Code details

best found code with parameters
q=8 k=4 n=103
minimum distance = 88

this is new optimal code

the previous bounds were 87/88
this is a projective code

We used the prescribed group of automorphisms with the following generators

0	0	7	0
7	0	0	0
0	7	0	0
0	0	0	7

0	0	0	7
7	0	0	0
0	0	7	0
0	7	0	0

This group makes 57 orbits of sizes:

4

12

12

12

12

12

12

12

12

12

12

6

12

6

4

1

4

4

4

4

4

4

12

12

12

12

12

12

12

12

12

12

6

12

12

12

12

12

12

6

12

12

12

12

12

12

12

12

12

12

12

12

12

12

12

12

12

The solution of the corresponding linear system of equations was found after less than 382 seconds:

0

1

0

0

0

0

0

0

1

1

0

0

1

0

0

1

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

1

0

0

0

0

1

0

0

0

0

0

0

0

0

0

1

0

0

0

1

0

0

0

0

0

15

15

15

15

15

11

15

15

15

15

15

15

15

15

3

7

15

15

3

15

15

15

7

11

15

15

7

15

7

15

11

11

15

11

15

11

11

15

15

15

15

15

15

11

15

7

7

15

11

15

15

15

11

7

11

11

15

This produces the following generator matrix

0	0	0	0	0	0	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	0	0	0	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	0	0	0	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	0	0	0	7	7	7	7	7	7	7	7	7
0	0	7	7	7	7	0	0	0	0	1	6	1	1	4	4	3	3	2	6	6	5	7	7	1	1	4	4	4	3	3	3	6	6	7	7	1	1	1	2	2	6	6	6	5	5	7	7	7	7	7	7	0	0	0	1	1	6	6	7	7	4	4	3	3	7	7	7	7	7	0	0	0	4	4	3	3	7	7	1	1	4	4	4	3	3	3	2	6	6	5	7	7	7	0	0	0	1	4	3	2	6	5
7	7	0	0	1	6	0	0	1	6	0	0	1	5	6	7	3	2	3	4	7	1	4	6	1	4	1	4	3	4	6	7	3	7	3	6	1	2	6	1	2	1	5	7	6	7	6	5	7	1	6	7	1	6	7	0	1	0	7	0	6	4	7	3	7	4	3	4	3	7	4	3	7	0	7	0	3	0	4	4	3	1	3	5	4	2	6	6	4	3	1	3	6	5	1	4	2	3	5	0	6	0	0
1	6	1	6	0	0	1	6	0	0	0	0	5	1	7	6	2	3	3	7	4	1	6	4	4	1	1	3	4	4	7	6	7	3	6	3	6	2	1	2	1	1	7	5	7	6	5	6	7	1	7	6	1	7	6	1	0	7	0	6	0	7	4	7	3	4	3	7	3	4	7	3	4	7	0	3	0	4	0	5	4	3	6	1	1	6	4	3	3	2	4	1	2	4	3	5	6	0	0	1	0	2	4

Which is a code with the following weight distribution
1y¹⁰³+2520x⁸⁸y¹⁵+1008x⁹²y¹¹+511x⁹⁶y⁷+56x¹⁰⁰y³