Code details

best found code with parameters
q=8 k=5 n=86
minimum distance = 69

this is a new code


the previous bounds were 68/72
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group makes 257 orbits of sizes:

5 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 10 20 10 5 1 5 5 5 5 5 5 20 20 20 20 20 10 20 20 20 20 10 20 20 20 10 20 20 10 20 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20


The solution of the corresponding linear system of equations was found after less than 80015 seconds:

0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 8 9 15 9 8 11 11 8 7 12 12 4 7 14 9 12 17 9 11 17 5 13 9 13 9 5 14 8 14 10 14 10 11 10 16 9 10 11 11 6 11 13 7 13 17 12 11 9 17 17 13 7 16 11 12 10 15 6 12 10 7 16 10 11 9 7 9 7 14 8 9 6 9 12 10 10 10 7 7 11 12 12 14 10 12 7 12 11 10 10 8 11 17 8 9 17 9 13 5 14 9 10 12 5 8 9 14 10 10 17 10 13 10 11 12 9 10 9 5 10 16 13 14 8 13 12 7 13 9 8 16 13 9 9 17 6 12 11 9 15 10 4 9 9 14 11 17 3 13 9 13 7 16 10 11 13 12 10 9 12 13 12 6 11 7 9 13 15 10 17 11 14 7 10 12 5 16 10 14 9 12 12 14 10 3 10 8 8 3 13 9 7 11 17 14 13 12 10 16 13 17 12 7 13 8 9 13 11 10 9 12 10 17 10 17 9 16 6 14 11 12 11 10 10 12 7 10 13 14 14 7 10 7 7 9 16 10 13 12 6 11 14 6 14 7 15 8 15 14 10 11 8 7 13 11 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 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 0 0 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 0 0 0 0 1 1 4 3 2 2 6 6 5 5 7 7 7 7 0 7 7 7 4 4 4 3 3 3 7 7 7 7 1 1 1 1 4 4 3 3 2 2 2 6 6 6 6 5 5 5 7 7 4 4 3 3 2 2 5 5 7 7 7 7 7 7 0 0 0 0 1 1 4 4 4 3 3 3 2 6 6 5
1 4 2 7 1 2 6 5 1 3 5 0 7 7 0 2 0 4 0 6 7 7 7 0 7 7 4 4 7 3 7 7 4 3 3 7 3 6 6 5 6 5 3 2 1 1 2 1 2 7 7 1 4 6 4 5 4 2 3 5 5 7 2 7 4 3 1 4 3 6 4 3 2 5 0 3 0 1 1 0 6 6 3 0 4 4
1 5 6 2 1 7 2 4 3 0 0 1 0 6 2 7 5 5 6 0 7 7 7 7 0 7 4 7 4 7 3 7 4 3 7 3 3 1 2 1 7 6 2 1 3 6 1 5 2 4 5 6 6 7 5 4 2 7 5 7 2 4 5 3 4 3 4 5 2 3 1 6 3 4 5 0 3 0 3 4 0 4 6 2 0 1
3 5 7 6 3 6 7 5 0 1 5 1 6 0 7 0 4 0 2 2 7 7 7 7 7 0 7 4 4 7 7 3 4 7 3 3 2 5 2 6 5 7 1 3 3 2 6 1 1 5 4 1 7 4 6 6 7 4 7 3 5 4 2 3 2 5 3 1 6 4 3 4 6 1 4 4 6 5 0 1 2 0 0 3 3 0



Which is a code with the following weight distribution
1y86+1575x69y17+1260x70y16+840x71y15+2555x72y14+2730x73y13+3780x74y12+3430x75y11+5320x76y10+4095x77y9+2100x78y8+2870x79y7+1120x80y6+532x81y5+280x82y4+280x83y3