Code details

best found code with parameters
q=23 k=3 n=24
minimum distance = 22

this is new optimal code


the previous bounds were -1/22
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

2 13 0
14 13 0
0 0 22

This group makes 61 orbits of sizes:

6 12 12 12 12 12 12 12 6 12 12 12 12 6 12 6 6 12 12 12 12 6 12 6 12 6 6 12 12 6 12 12 6 12 12 6 12 6 12 12 6 6 12 6 12 12 6 12 3 12 6 6 6 12 6 6 6 6 6 1 3


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

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 1 0 0 2 0 2 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 0 0 0 0 0 2 0 2 0 0 2 0 0 0 0 0 0 0 2 1 2 0 0


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
16 4 1 9 21 5 0 0 16 4 6 10 9 17 12 12 15 5 1 10 20 20 21 15
16 1 4 21 9 5 6 17 5 12 0 9 10 0 4 15 12 16 15 20 10 21 20 1



Which is a code with the following weight distribution
1y24+6072x22y2+528x23y1+5566x24