Code details

best found code with parameters
q=8 k=5 n=98
minimum distance = 80

this is new code


the previous bounds were 78/83
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:

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 14 0 14 14 12 14 12 10 18 10 0 14 12 14 12 12 10 10 10 10 18 18 10 12 14 8 8 16 12 16 8 8 12 8 16 16 4 16 12 16 16 12 12 10 12 12 16 16 6 12 8 16 14 12 12 18 12 10 14 10


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y98+2744x80y18+5488x82y16+2548x84y14+10976x86y12+6517x88y10+3087x90y8+686x92y6+686x94y4+35x98