Code details

best found code with parameters
q=19 k=3 n=147
minimum distance = 138

this is new optimal code


the previous bounds were -1/138
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

18 0 0
0 18 0
0 0 18

14 0 0
0 4 0
0 0 18

This group makes 33 orbits of sizes:

1 2 18 18 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 18 18 18 18 18 18 18 18 18


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

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



Which is a code with the following weight distribution
1y147+3402x138y9+1620x139y8+810x140y7+486x141y6+162x143y4+54x145y2+324x147