Code details

best found code with parameters
q=2 k=10 n=177
minimum distance = 84

this is new optimal code


the previous bounds were 82/84
this is not a projective code, the bound was 2


We used the prescribed group of automorphisms with the following generators


1 0 1 0 1 0 0 1 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 1 0 0 0 1 0 0
1 0 1 1 1 1 0 1 0 0
1 1 0 0 0 0 0 0 1 0
0 0 1 0 0 0 1 1 1 1
1 1 0 1 0 1 0 0 1 1
1 0 1 1 0 1 0 1 1 0
0 0 1 0 1 1 0 0 0 0
1 0 1 0 1 0 1 1 0 0

This group make 51 orbits of sizes:

21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 7 21 21 21 21 21 21 21 7 21 21 21 21 21 21 21 21 21 21 21 21 21 1


The solution of the corresponding linear system of equations was found after less than 5000 seconds:

0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 89 93 93 93 93 93 93 77 89 89 85 89 89 93 93 89 93 89 89 93 93 93 93 77 93 77 93 85 89 89 93 89 89 93 93 77 77 77 77 89 89 93 93 77 93 77 93 93 49 77 93


This produces the following generator matrix

0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0
0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0
0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1
0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1
0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0
1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0
1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1
0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1
1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0



Which is a code with the following weight distribution
1y177+490x84y93+294x88y89+42x92y85+196x100y77+1x128y49