Code details

best found code with parameters
q=3 k=8 n=65
minimum distance = 37

this is new code


the previous bounds were 36/39
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 1 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 0 9 25 23 21 19 26 15 24 8 24 22 20 27 16 23 21 21 21 21 23 14 23 25 23 23 23 25 16 23 25 16 18 25 16 16 25 27 25 16 18 18 27 27 18 27 18 20 20 20 20 20 22 22 17 17 26 28 28 19 28 21 19 21 21 21 21 23 23 23 23 25 25


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



Which is a code with the following weight distribution
1y65+336x37y28+560x38y27+224x39y26+756x40y25+140x41y24+1064x42y23+168x43y22+816x44y21+560x45y20+336x46y19+560x47y18+224x48y17+672x49y16+16x50y15+112x51y14+14x56y9+2x57y8