Code details

best found code with parameters
q=8 k=4 n=112
minimum distance = 96

this is new optimal code


the previous bounds were 95/96
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group makes 9 orbits of sizes:

112 112 112 112 7 64 64 1 1


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

0 0 1 0 0 0 0 0 0 0 16 16 12 16 16 0 0 0


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y112+2401x96y16+1568x100y12+126x112