Code details

best found code with parameters
q=3 k=7 n=46
minimum distance = 26

this is new code


the previous bounds were 25/27
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

This group make 69 orbits of sizes:

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 10 20 20 10 20 5 20 20 20 5 10 20 20 20 20 20 20 4 20 20 20 20 20 20 5 20 20 10 20 20 20 20 20 20 5 10 20 20 2 20 10 5 5 4 10 5 20 5 10 2 1


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

0 0 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 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 0 1 16 19 14 20 14 18 18 10 14 14 16 15 13 19 9 13 14 19 13 18 20 16 13 15 9 13 16 14 11 15 18 10 13 20 18 11 20 15 16 18 20 15 14 14 20 12 18 16 7 19 17 7 16 15 15 18 16 12 13 15 20 18 18 12 18 20 20 5 20


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y46+236x26y20+160x27y19+350x28y18+10x29y17+248x30y16+280x31y15+320x32y14+220x33y13+100x34y12+80x35y11+80x36y10+80x37y9+20x39y7+2x41y5