Code details

best found code with parameters
q=13 k=3 n=23
minimum distance = 20

this is new optimal code


the previous bounds were -1/20
this is a projective code


We used the prescribed group of automorphisms with the following generators


12 0 0
0 12 0
0 0 12

12 0 0
0 6 0
0 0 3

This group makes 51 orbits of sizes:

1 1 4 1 4 2 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 2 4 4 4 4 4 4 2 4 4 4 4 4 4 2 4 4 4 4 4 4 2 4 4 4 4


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

1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 3 3 0 0 0 3 3 3 1 3 3 2 0 0 3 3 2 0 3 0 1 3 2 1 2 0 1 3 3 1 1 3 0 2 2 3 3 0 3 2 2 0 1 3 2 3 3


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y23+840x20y3+516x21y2+312x22y1+528x23