Code details

best found code with parameters
q=17 k=3 n=239
minimum distance = 224

this is new optimal code


the previous bounds were -1/224
this is a projective code


We used the prescribed group of automorphisms with the following generators


16 0 0
0 0 16
0 16 0

7 0 0
0 11 0
0 0 3

This group makes 51 orbits of sizes:

2 2 1 8 4 8 8 4 8 8 8 8 8 8 8 8 4 8 8 4 4 8 8 8 8 4 4 8 8 8 8 4 8 4 4 8 8 8 8 4 4 8 4 4 4 4 8 4 4 2 4


The solution of the corresponding linear system of equations was found after less than 8003 seconds:

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



Which is a code with the following weight distribution
1y239+1408x224y15+2992x225y14+448x226y13+64x239