Code details

best found code with parameters
q=19 k=3 n=225
minimum distance = 212

this is new optimal code


the previous bounds were -1/212
this is a projective code


We used the prescribed group of automorphisms with the following generators


18 0 0
0 0 18
0 18 0

14 0 0
0 8 0
0 0 2

18 0 0
0 18 0
0 0 18

0 0 18
18 0 0
0 18 0

This group makes 33 orbits of sizes:

3 9 3 9 9 18 9 9 18 18 18 18 18 9 9 9 9 18 18 9 18 18 9 9 9 18 9 9 9 9 18 3 3


The solution of the corresponding linear system of equations was found after less than 500 seconds:

1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 11 13 11 11 13 13 12 10 13 12 11 13 13 13 13 13 13 10 13 9 11 13 13 12 12 13 11 12 13 0 11 11 12


This produces the following generator matrix

0 0 18 0 0 0 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 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 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 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 0 0 0 0 0 0 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
0 18 0 18 18 18 0 0 0 18 6 12 18 6 12 18 1 13 6 17 12 5 7 11 1 13 2 16 14 3 3 8 17 15 15 5 7 11 4 10 9 9 18 6 3 3 12 15 15 9 9 18 6 3 3 12 15 15 9 9 1 13 2 16 14 3 3 8 17 15 15 5 7 11 4 10 9 9 1 13 2 16 14 3 3 8 17 15 15 5 7 11 4 10 9 9 1 13 2 16 14 3 3 8 17 15 15 5 7 11 4 10 9 9 18 2 16 14 6 8 12 4 10 18 2 16 14 6 8 12 4 10 1 1 13 13 2 16 14 8 17 17 5 5 7 7 11 11 4 10 1 1 13 13 2 16 14 8 17 17 5 5 7 7 11 11 4 10 18 2 16 14 6 8 12 4 10 18 2 16 14 6 8 12 4 10 18 1 13 6 17 12 5 7 11 18 1 13 6 17 12 5 7 11 18 18 18 18 18 18 0 0 0 0 0 0 1 13 17 5 7 11 18 6 12
18 0 0 18 6 12 18 6 12 0 0 0 12 6 18 5 7 13 17 6 11 18 1 12 10 16 15 13 3 14 5 9 9 2 11 3 4 15 7 1 8 17 3 15 18 9 9 6 15 3 12 15 9 3 12 3 18 9 6 15 4 10 9 7 15 8 17 3 3 14 5 15 16 9 1 13 2 11 3 9 17 15 5 1 10 11 2 16 7 14 15 8 9 3 13 4 9 15 5 3 11 16 7 17 8 13 4 2 3 14 15 9 1 10 8 6 4 12 2 18 14 16 10 2 18 16 6 14 12 8 10 4 8 5 14 11 7 5 13 1 7 4 1 16 2 17 13 10 17 11 2 17 8 5 1 17 7 13 1 16 13 10 14 11 7 4 11 5 4 8 6 14 16 2 10 18 12 16 2 18 8 10 14 4 12 6 1 18 6 13 17 7 11 12 5 11 13 1 5 12 17 6 7 18 1 13 17 5 7 11 1 13 17 5 7 11 0 0 0 0 0 0 6 18 12



Which is a code with the following weight distribution
1y225+3564x212y13+1026x213y12+1458x214y11+486x215y10+162x216y9+162x225