Code details

best found code with parameters
q=19 k=3 n=285
minimum distance = 269

this is new optimal code


the previous bounds were -1/269
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:

1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 16 15 0 16 16 15 16 16 16 16 16 14 15 15 16 15 15 14 15 14 15 14 16 12 13 12 15 15 15 16 16 16 16 16 12 16 15 16 16


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



Which is a code with the following weight distribution
1y285+3186x269y16+2232x270y15+756x271y14+216x272y13+396x273y12+72x285