Code details

best found code with parameters
q=11 k=3 n=89
minimum distance = 80

this is new optimal code


the previous bounds were -1/80
this is a projective code


We used the prescribed group of automorphisms with the following generators


9 9 7
8 8 0
6 4 2

This group makes 19 orbits of sizes:

8 8 8 4 8 8 8 8 8 8 8 8 8 4 8 8 8 4 1


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

1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 9 9 3 7 9 9 8 7 8 6 8 9 9 9 8 9 9 8 9


This produces the following generator matrix

0 10 10 10 10 10 10 10 0 0 10 10 10 10 10 10 0 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 0 10 10 10 0 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 10 10
0 0 10 1 8 4 3 5 10 10 0 10 10 1 8 5 10 0 0 9 7 6 5 5 10 0 0 2 2 7 5 5 0 1 8 4 7 7 3 5 0 1 8 4 9 9 3 5 1 8 2 4 4 3 3 6 10 10 4 3 10 10 2 2 4 9 9 3 10 10 4 9 9 7 7 3 10 1 1 8 8 2 9 7 1 8 2 7 10
10 5 3 4 10 3 9 0 3 6 2 8 5 5 8 1 4 0 7 7 2 9 2 5 1 10 4 8 5 10 4 6 8 8 7 1 7 6 6 3 3 6 6 0 2 9 0 9 3 3 2 8 2 8 4 10 8 6 5 3 0 7 0 9 10 4 5 7 1 9 9 0 3 0 8 2 10 1 9 0 4 1 10 5 10 2 7 4 7



Which is a code with the following weight distribution
1y89+760x80y9+250x81y8+160x82y7+80x83y6+80x86y3