Code details

best found code with parameters
q=19 k=3 n=172
minimum distance = 162

this is new optimal code


the previous bounds were -1/162
this is a projective code


We used the prescribed group of automorphisms with the following generators


18 0 0
0 18 0
0 0 18

11 0 11
11 11 0
0 0 11

This group makes 21 orbits of sizes:

19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 1


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

1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 9 9 9 9 10 9 10 9 10 10 10 10 9 9 10 0 9 10 10 10


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y172+3420x162y10+3078x163y9+18x171y1+342x172