Code details

best found code with parameters
q=17 k=3 n=154
minimum distance = 144

this is new optimal code


the previous bounds were -1/144
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:

0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 0 1 10 10 9 9 9 10 9 10 1 10 9 10 10 9 9 9 9 10 10 10 9 10 10 10 1 10 9 9 9 10 9


This produces the following generator matrix

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 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 16 16 16 16 16 16 16 16 16 16 16 16 0 0 16 16 16 16
16 16 8 8 16 16 14 14 10 10 2 2 6 6 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 5 5 11 11 3 3 13 13 8 8 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 5 5 10 10 2 2 13 13 9 9 16 16 0 0 1 9 16 16 0 0 12 4 15 15 15 15 10 10 2 2 7 7 7 7 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 8 16 8 14 6 16 8 10 2 10 2 16 8 14 6 1 9 16 8 15 7 15 7 16 8 1 9 5 13 16 8 11 3 11 3 16 8 5 13 11 3 5 13 16 8 16 8 5 13 11 3 1 9 5 13 10 2 10 2 5 13 1 9 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 14 6 15 7 11 3 11 3 15 7 14 6 1 9 15 7 0 0 12 4 12 4 0 0 14 1 9 6 1 9 1 9 14 1 9 6 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
1y154+2448x144y10+2176x145y9+288x153y1