Code details

best found code with parameters
q=3 k=8 n=64
minimum distance = 37

this is new code


the previous bounds were 36/38
this is a projective code


We used the prescribed group of automorphisms with the following generators


2 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 2

2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2
0 2 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0 0 0 0
0 0 0 0 2 0 0 0
0 0 0 0 0 2 0 0
0 0 0 0 0 0 2 0

This group make 72 orbits of sizes:

7 14 28 56 56 56 8 56 1 14 28 56 56 56 56 8 56 56 8 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 28 28 56 28 28 56 56 56 56 56 56 56 28 56 28 56 56 56 28 28 28 28 14 14


The solution of the corresponding linear system of equations was found after less than 10 seconds:

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 24 22 20 18 25 14 23 8 24 22 20 27 16 23 21 21 21 21 23 23 14 25 23 23 23 16 16 23 25 25 18 16 25 16 16 27 25 25 18 27 18 18 27 27 18 20 20 20 20 20 22 22 25 16 16 27 18 27 18 20 27 20 20 20 20 22 22 22 22 24 24


This produces the following generator matrix

0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 0 0 2 2 2 2 1 1 1 1 0 0 2 2 2 2 1 1 1 1 2 2 1 1 0 0 2 2 2 2 1 1 1 1 0 0 2 2 2 2 1 1 1 1
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 0 2 1 1 0 2 2 1 2 1 0 2 1 1 0 2 2 1 1 1 2 2 2 1 0 2 2 1 0 2 1 1 2 1 0 2 2 1 0 2 1 1
2 2 1 1 1 1 2 2 2 1 2 1 1 2 1 2 2 1 2 1 2 1 1 1 0 2 2 0 1 2 1 2 2 2 0 1 1 0 2 1 2 1 2 1 2 1 2 0 1 2 1 1 0 2 1 2 1 0 2 1 2 2 0 1
2 1 1 2 1 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 1 1 1 2 2 0 1 2 0 2 2 2 2 1 1 0 2 1 0 1 2 1 1 2 2 2 2 1 0 1 2 1 1 0 1 1 1 2 0 2 1 2 2 0
2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 2 1 2 1 2 1 2 1 0 1 2 2 2 1 0 2 1 2 0 2 1 1 1 2 0 2 1 2 1 2 1 1 1 2 0 2 0 2 1 1 2 2 2 1 0 1 0 1 2



Which is a code with the following weight distribution
1y64+896x37y27+896x39y25+112x40y24+896x41y23+448x42y22+256x43y21+1120x44y20+896x46y18+896x48y16+128x50y14+16x56y8