Code details

best found code with parameters
q=16 k=3 n=65
minimum distance = 60

this is new optimal code


the previous bounds were -1/60
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:

0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 5 5 1 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 5 1 1 5 5 1 5 5 1 5 5 5 5 5


This produces the following generator matrix

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 1 8 14 4 5 7 2 13 10 11 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
9 3 6 12 15 2 10 4 14 13 11 1 5 8 7 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
1y65+3120x60y5+975x64y1