Code details

best found code with parameters
q=23 k=3 n=484
minimum distance = 462

this is new optimal code


the previous bounds were -1/462
this is a projective code


We used the prescribed group of automorphisms with the following generators


10 0 0
0 21 0
0 0 10

14 0 0
0 0 14
0 14 0

0 0 6
6 0 0
0 6 0

This group makes 33 orbits of sizes:

3 6 4 12 12 12 12 12 12 12 12 12 12 24 24 24 24 24 24 24 24 12 24 24 24 24 12 24 24 24 12 12 12


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

0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 22 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 21 21 21 21 22 21 21 21 22 22 22


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



Which is a code with the following weight distribution
1y484+1452x462y22+10648x463y21+66x484