Code details

best found code with parameters
q=3 k=7 n=61
minimum distance = 36

this is new code


the previous bounds were 35/37
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 2 0 0 0 0
2 0 0 0 0 0 0
0 2 0 0 0 0 0
0 0 0 0 0 2 0
0 0 0 2 0 0 0
0 0 0 0 2 0 0
0 0 0 0 0 0 2

1 0 0 0 0 0 0
0 2 0 0 0 0 0
0 0 2 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 2 0
0 0 0 0 0 0 2

This group make 67 orbits of sizes:

1 3 6 6 12 4 4 4 3 6 6 12 6 12 12 24 6 12 12 24 12 24 24 24 24 6 12 12 24 12 12 12 24 24 24 12 24 12 24 12 24 24 24 24 24 24 24 24 24 24 4 8 24 24 24 24 24 24 8 8 8 24 24 24 24 24 24


The solution of the corresponding linear system of equations was found after less than 46 seconds:

1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 24 19 9 25 24 25 15 15 19 21 25 18 25 18 25 18 25 18 25 18 25 18 19 21 21 25 12 25 21 25 21 21 19 15 24 25 21 19 24 19 15 19 24 15 16 21 21 25 21 21 25 24 19 18 18 25 24 24 16 15 15 16 24 24 15 24 16


This produces the following generator matrix

0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 2 2 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1
0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1
0 0 0 2 2 0 0 0 0 0 0 0 0 2 2 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 0 1 0 2 2 1 0 2 0 1 2 1 0 2 0 1 2 1 0 1 0 2
0 2 2 0 0 0 0 0 0 0 0 0 0 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 2 1 2 1 0 2 0 2 1 1 0 2 0 1 2 2 0 1 0 2 1 2 0 1 0
2 2 1 2 1 2 1 2 1 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 2 2 1 2 1 2 1 1 2 1 2 1 2 2 1 1 2 2 1 1 2



Which is a code with the following weight distribution
1y61+316x36y25+426x37y24+444x40y21+252x42y19+312x43y18+160x45y16+240x46y15+24x49y12+12x52y9