Code details

best found code with parameters
q=17 k=3 n=182
minimum distance = 170

this is new optimal code


the previous bounds were -1/170
this is a projective code


We used the prescribed group of automorphisms with the following generators


2 0 0
0 8 0
0 0 16

This group makes 47 orbits of sizes:

1 1 2 1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 2 2 2 2


The solution of the corresponding linear system of equations was found after less than 50000 seconds:

1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 9 9 12 6 11 11 12 11 12 12 11 12 12 10 7 11 8 12 10 5 11 6 10 12 12 12 12 12 12 12 12 12 12 12 6 11 8 11 12 12 9 12 9 4 12 12 12


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



Which is a code with the following weight distribution
1y182+2592x170y12+1024x171y11+384x172y10+96x173y9+256x174y8+128x175y7+272x176y6+128x177y5+32x178y4