Code details

best found code with parameters
q=8 k=4 n=103
minimum distance = 88

this is new optimal code


the previous bounds were 87/88
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group makes 57 orbits of sizes:

4 12 12 12 12 12 12 12 12 12 12 6 12 6 4 1 4 4 4 4 4 4 12 12 12 12 12 12 12 12 12 12 6 12 12 12 12 12 12 6 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12


The solution of the corresponding linear system of equations was found after less than 382 seconds:

0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 15 15 15 15 15 11 15 15 15 15 15 15 15 15 3 7 15 15 3 15 15 15 7 11 15 15 7 15 7 15 11 11 15 11 15 11 11 15 15 15 15 15 15 11 15 7 7 15 11 15 15 15 11 7 11 11 15


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y103+2520x88y15+1008x92y11+511x96y7+56x100y3