Code details

best found code with parameters
q=17 k=3 n=219
minimum distance = 205

this is new optimal code


the previous bounds were -1/205
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

4 0 0
0 12 0
0 0 12

16 0 0
0 16 0
0 0 16

This group makes 31 orbits of sizes:

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


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

1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 14 13 0 14 14 14 13 14 14 13 12 14 13 14 11 12 11 13 13 13 10 13 10 13 14 13 14 14 13 14 14


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y219+1968x205y14+1920x206y13+288x207y12+384x208y11+288x209y10+64x219