Code details

best found code with parameters
q=23 k=3 n=254
minimum distance = 242

this is new optimal code


the previous bounds were -1/242
this is a projective code


We used the prescribed group of automorphisms with the following generators


17 0 0
0 17 17
17 0 17

This group makes 25 orbits of sizes:

23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 1


The solution of the corresponding linear system of equations was found after less than 100 seconds:

0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 12 12 11 12 11 12 11 11 12 11 12 12 11 12 0 11 11 11 12 12 11 12 12 11 1


This produces the following generator matrix

22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 0
0 0 22 22 16 16 1 1 18 18 10 10 3 3 14 14 17 17 5 13 13 11 11 0 0 16 16 4 4 19 19 10 10 21 17 17 8 8 7 7 12 12 5 5 11 11 0 0 22 22 2 2 4 4 18 18 19 19 3 3 9 9 21 21 8 8 13 11 11 2 2 16 16 18 18 6 6 14 21 21 17 17 8 8 7 7 15 15 13 13 11 11 22 22 2 2 1 1 18 18 10 10 9 9 8 7 7 12 12 15 15 5 5 11 11 22 22 16 16 4 4 19 19 6 6 9 9 14 14 12 15 15 5 5 13 13 11 11 0 0 22 22 4 4 1 1 6 6 3 3 17 8 8 7 7 12 12 15 15 13 13 0 0 1 18 18 19 19 6 6 10 10 9 9 14 14 21 21 7 7 12 12 13 13 0 0 2 2 19 6 6 10 10 3 3 9 9 14 14 17 17 8 8 15 15 5 5 2 16 16 4 4 1 1 18 18 6 6 3 3 9 9 21 21 17 17 12 12 5 5 22 2 2 16 16 4 4 1 1 19 19 10 10 3 3 14 14 21 21 7 7 15 15 22
0 22 2 11 16 13 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 6 8 3 21 0 22 2 11 16 13 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 6 8 4 5 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 16 13 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 18 12 20 19 7 3 21 0 22 2 11 16 13 6 8 4 5 9 14 1 15 10 17 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 6 8 4 5 9 14 1 15 20 19 7 3 21 0 22 2 11 16 13 6 8 4 5 9 14 1 15 10 17 18 12 20 19 7 3 21 0 22 2 11 16 13 6 8 4 5 9 14 1 15 10 17 18 12 0



Which is a code with the following weight distribution
1y254+6072x242y12+5566x243y11+22x253y1+506x254