Code details

best found code with parameters
q=13 k=3 n=44
minimum distance = 39

this is new optimal code


the previous bounds were -1/39
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 12
12 0 0
0 12 0

11 0 0
0 5 0
0 0 2

This group makes 9 orbits of sizes:

3 12 16 48 48 16 12 16 12


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

0 1 1 0 0 0 0 1 0 4 5 4 3 5 1 4 2 0


This produces the following generator matrix

0 0 0 0 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
12 12 12 12 0 0 0 0 12 9 3 6 12 12 12 12 9 9 9 9 3 3 3 3 6 6 6 6 2 2 2 2 5 5 5 5 11 11 11 11 8 8 8 8
12 9 3 6 12 9 3 6 0 0 0 0 12 9 3 6 12 9 3 6 12 9 3 6 12 9 3 6 1 4 10 7 1 4 10 7 1 4 10 7 1 4 10 7



Which is a code with the following weight distribution
1y44+720x39y5+372x40y4+576x41y3+192x42y2+192x43y1+144x44