Code details

best found code with parameters
q=23 k=3 n=277
minimum distance = 264

this is new optimal code


the previous bounds were -1/264
this is a projective code


We used the prescribed group of automorphisms with the following generators


22 0 0
0 0 22
0 22 0

22 0 0
0 0 22
0 22 0

6 5 0
13 17 0
0 0 22

This group makes 37 orbits of sizes:

12 24 24 12 24 24 12 24 24 24 12 12 12 12 12 12 12 12 12 12 12 12 24 12 12 12 24 12 24 24 12 6 12 12 6 12 1


The solution of the corresponding linear system of equations was found after less than 300 seconds:

1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 1 1 13 13 12 12 12 13 13 13 12 12 13 12 13 12 12 13 12 12 13 12 13 12 13 12 13 13 13 13 12 1 12 1 13 12 13 13 12


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y277+6072x264y13+5566x265y12+528x276y1