Code details

best found code with parameters
q=19 k=3 n=324
minimum distance = 306

this is new optimal code


the previous bounds were -1/306
this is a projective code


We used the prescribed group of automorphisms with the following generators


14 18 5
14 0 3
15 12 1

This group makes 21 orbits of sizes:

36 36 36 36 36 36 36 36 2 36 36 2 2 2 2 2 1 2 2 2 2


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

1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 17 17 17 17 17 18 17 17 17 17 18 18 18 18 18 18 0 18 18 18 0


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



Which is a code with the following weight distribution
1y324+972x306y18+5832x307y17+54x324