Code details

best found code with parameters
q=8 k=4 n=85
minimum distance = 72

this is a new optimal code


the previous bounds were 71/72
this is not a projective code, the bound was 3


We used the prescribed group of automorphisms with the following generators


1 5 6 1
1 2 5 1
5 2 2 3
5 4 5 0

This group makes 41 orbits of sizes:

9 9 9 9 18 18 18 2 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 9 18 18 18 18 18 18 18 18 2 18 18 9 9 2 9 2 1


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

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 0 1 0 0 0 0 0 5 9 11 3 11 11 11 11 11 1 11 13 13 13 13 13 9 13 13 13 13 9 11 11 11 11 9 11 13 5 11 11 13 13 13 9 11 9 9 9 9


This produces the following generator matrix

0 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 7 7 7 7 7 7 7
7 7 7 0 0 1 1 4 4 2 2 6 6 6 7 7 7 7 0 7 0 0 1 4 4 4 3 3 3 2 2 2 6 5 7 7 0 7 0 1 1 4 3 3 3 2 2 6 6 6 5 5 5 7 7 7 0 0 1 1 1 1 4 4 4 2 2 6 6 5 7 7 4 4 5 5 7 7 0 0 1 1 3 5 5
2 2 7 1 3 3 6 6 7 1 3 6 5 7 1 1 3 5 7 3 3 5 3 1 4 6 4 6 5 0 1 3 7 5 3 5 7 7 1 2 6 7 4 6 5 7 7 4 6 5 4 4 7 6 3 7 3 5 0 3 5 5 0 0 1 0 3 1 6 6 4 3 4 4 5 5 5 5 4 4 7 7 3 1 1
1 5 6 4 5 2 5 3 7 7 2 4 4 5 3 7 7 4 3 5 3 6 3 4 4 7 2 6 2 5 5 7 3 2 1 1 2 1 6 5 7 1 6 3 1 3 2 6 6 5 1 2 1 4 6 5 7 0 2 0 1 3 5 7 0 6 4 5 3 4 2 0 1 1 6 6 0 6 4 5 2 7 1 3 6



Which is a code with the following weight distribution
1y85+1386x72y13+1778x74y11+490x76y9+189x80y5+126x82y3+126x84y1