Code details

best found code with parameters
q=3 k=7 n=59
minimum distance = 34

this is new code


the previous bounds were 33/36
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

This group make 63 orbits of sizes:

4 8 16 4 4 2 8 8 16 8 32 16 16 2 16 32 32 8 16 8 1 8 16 32 8 8 4 16 16 16 16 16 32 16 32 16 4 32 32 32 8 32 8 32 16 32 32 32 16 16 32 32 32 32 16 8 32 8 8 32 16 8 4


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

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 11 23 23 23 17 25 25 13 19 25 19 25 13 18 18 24 18 21 24 21 10 22 22 19 19 25 12 18 21 18 18 15 24 15 18 24 23 20 23 23 14 17 23 23 23 23 14 14 14 23 15 18 18 18 24 22 18 24 24 22 19 13 23


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y59+84x34y25+256x35y24+408x36y23+128x37y22+64x38y21+64x39y20+208x40y19+516x41y18+72x42y17+128x44y15+176x45y14+64x46y13+8x47y12+8x48y11+2x49y10