Code details

best found code with parameters
q=8 k=5 n=103
minimum distance = 84

this is new code


the previous bounds were 83/88
this is a projective code


We used the prescribed group of automorphisms with the following generators


7 0 0 0 0
0 0 7 0 0
0 7 0 0 0
0 0 0 0 7
0 0 0 7 0

4 0 0 0 0
0 5 0 0 0
0 0 6 0 0
0 0 0 5 0
0 0 0 0 4

This group makes 61 orbits of sizes:

2 7 2 14 14 98 7 98 98 98 49 1 14 49 14 98 98 98 98 98 98 98 98 98 49 98 49 98 49 98 49 98 49 98 49 98 49 98 49 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98


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

1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 17 4 17 17 14 17 14 19 11 11 4 17 14 17 14 14 19 19 11 11 11 11 11 14 11 16 12 8 8 16 12 8 8 16 12 8 16 16 12 12 16 16 4 7 12 8 16 12 15 12 12 16 11 12 16 19 12 15 15 11


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y103+2744x84y19+490x86y17+5488x87y16+2058x88y15+3430x89y14+7546x91y12+6517x92y11+3087x95y8+686x96y7+721x99y4