Code details

best found code with parameters
q=19 k=3 n=52
minimum distance = 48

this is new optimal code


the previous bounds were -1/48
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 18
18 0 0
0 18 0

11 0 0
0 2 0
0 0 2

This group makes 39 orbits of sizes:

3 6 4 12 12 12 12 12 12 12 12 12 12 12 12 12 12 6 12 12 12 12 12 6 12 12 6 12 12 12 12 6 12 6 4 6 4 6 6


The solution of the corresponding linear system of equations was found after less than 100 seconds:

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


This produces the following generator matrix

18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
1 1 2 2 6 6 15 15 11 11 10 10 1 1 14 14 3 3 12 12 5 5 10 10 2 2 8 8 8 8 17 17 17 17 11 11 16 16 14 14 6 6 15 15 5 5 7 7 3 3 12 12
16 7 3 12 8 17 8 17 3 12 16 7 6 15 8 17 13 4 13 4 8 17 6 15 1 10 1 16 7 10 1 16 7 10 1 10 13 4 3 12 2 11 2 11 3 12 13 4 6 15 6 15



Which is a code with the following weight distribution
1y52+3528x48y4+864x49y3+108x50y2+1800x51y1+558x52