Code details

best found code with parameters
q=23 k=3 n=461
minimum distance = 440

this is new optimal code


the previous bounds were -1/440
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 18 0
18 0 0
0 0 18

22 0 0
0 22 0
0 0 22

16 0 0
0 5 0
0 0 16

This group makes 85 orbits of sizes:

1 2 4 2 4 4 4 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 4 8 8 8 8 8 8 8 8 8 8 8 4 8 8 8 8 8 8 8 8 8 8 8 4 8 8 8 8 8 8 8 8 8 8 8 4 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 4 4 4 4 4 4


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

1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 20 21 21 21 20 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 21 21 20 21 21 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 20 20 20 21 21 20 20 20 20 20 20 20 20 20 20 20 21 21 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 0


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y461+2728x440y21+8470x441y20+880x442y19+88x461