Code details

best found code with parameters
q=8 k=5 n=119
minimum distance = 98

this is a new code


the previous bounds were 97/101
this is not a projective code, the bound was 2


We used the prescribed group of automorphisms with the following generators


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

This group makes 121 orbits of sizes:

39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 1


The solution of the corresponding linear system of equations was found after less than 20 seconds:

0 0 1 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 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 1 0 0 0 0 0 0 0 0 0 2 9 19 21 21 9 19 15 11 15 14 19 14 11 19 19 14 15 20 18 19 10 7 20 11 13 21 17 14 15 21 14 11 10 15 15 15 19 14 4 8 20 11 11 15 14 11 18 11 17 15 16 14 12 14 14 18 14 18 18 15 19 21 10 15 15 19 18 13 12 16 17 18 15 10 17 20 8 18 10 13 16 14 15 12 15 12 7 19 18 11 14 16 11 20 18 17 19 14 11 14 11 14 16 20 12 18 14 17 11 16 14 16 11 19 17 19 11 12 16 13 0


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y119+1365x98y21+1638x99y20+3549x100y19+3003x101y18+1911x102y17+2184x103y16+4095x104y15+4914x105y14+1092x106y13+1638x107y12+4095x108y11+1365x109y10+546x110y9+546x111y8+546x112y7+273x115y4+7x119