Code details

best found code with parameters
q=11 k=3 n=21
minimum distance = 18

this is new optimal code


the previous bounds were -1/18
this is a projective code


We used the prescribed group of automorphisms with the following generators


10 5 5
5 2 2
2 2 4

This group makes 19 orbits of sizes:

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7


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

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


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y21+630x18y3+210x19y2+210x20y1+280x21