Code details

best found code with parameters
q=19 k=3 n=124
minimum distance = 116

this is new optimal code


the previous bounds were -1/116
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 18
18 0 0
0 18 0

11 0 0
0 2 0
0 0 2

This group makes 39 orbits of sizes:

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


The solution of the corresponding linear system of equations was found after less than 500 seconds:

0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 4 5 7 7 7 7 8 7 8 8 8 7 2 7 8 8 8 6 8 7 2 8 2 6 7 5 6 2 8 7 8 8 8 7 0 6 7 6 8


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y124+2808x116y8+2196x117y7+540x118y6+324x119y5+54x120y4+864x122y2+72x124