Code details

best found code with parameters
q=19 k=3 n=105
minimum distance = 98

this is new optimal code


the previous bounds were -1/98
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 16
16 0 0
0 16 0

13 0 0
0 13 0
0 0 13

6 0 0
0 12 0
0 0 18

This group makes 45 orbits of sizes:

3 9 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 3 3 9 9


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

1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 5 6 3 7 6 6 6 6 4 7 7 5 7 7 2 2 7 7 3 5 7 7 7 7 5 7 7 1 7 6 7 7 2 5 4 5 7 7 7 6 6 2 0 0 6


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y105+3078x98y7+1458x99y6+864x100y5+324x101y4+216x102y3+540x103y2+162x104y1+216x105