Code details

best found code with parameters
q=16 k=3 n=93
minimum distance = 86

this is new optimal code


the previous bounds were -1/86
this is a projective code


We used the prescribed group of automorphisms with the following generators


15 0 0
0 0 15
0 15 0

9 0 0
0 6 0
0 0 12

This group makes 37 orbits of sizes:

2 10 5 1 10 5 10 10 10 5 10 10 10 5 10 5 5 5 10 10 10 10 10 5 10 10 5 5 10 5 5 10 10 5 5 5 5


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

1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 7 6 7 7 6 7 2 7 7 5 7 7 7 5 7 5 5 5 7 7 7 7 7 7 2 2 7 7 2 7 7 2 6 7 7 7 7


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y93+2520x86y7+450x87y6+375x88y5+750x91y2