Code details

best found code with parameters
q=8 k=4 n=117
minimum distance = 100

this is a new optimal code


the previous bounds were 99/100
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group makes 45 orbits of sizes:

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13


The solution of the corresponding linear system of equations was found after less than 20 seconds:

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 17 13 17 13 17 17 17 13 17 17 17 17 9 17 9 17 17 17 17 17 17 13 13 13 13 13 13 9 5 13 13 13 17 17 17 13 17 17 13 17 17 17 5 17 13


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y117+2275x100y17+1365x104y13+273x108y9+182x112y5