Code details

best found code with parameters
q=19 k=3 n=191
minimum distance = 180

this is new optimal code


the previous bounds were -1/180
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 18 0
18 0 0
0 0 18

18 0 0
0 18 0
0 0 18

14 0 0
0 4 0
0 0 18

This group makes 33 orbits of sizes:

1 2 18 18 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 18 18 18 18 18 18 18 18 18


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

0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 11 1 11 11 11 11 10 10 10 10 11 11 10 11 11 10 11 11 10 10 10 10 11 10 11 11 10 1 11 11 10 10 10


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y191+3420x180y11+3078x181y10+360x190y1