Code details

best found code with parameters
q=16 k=3 n=231
minimum distance = 216

this is new optimal code


the previous bounds were -1/216
this is a projective code


We used the prescribed group of automorphisms with the following generators


15 0 0
0 15 0
0 0 15

10 15 15
4 0 7
7 1 5

This group makes 13 orbits of sizes:

21 21 21 21 21 21 21 21 21 21 21 21 21


The solution of the corresponding linear system of equations was found after less than 500 seconds:

1 1 1 1 1 1 1 1 1 1 0 1 0 11 15 15 11 15 15 15 15 15 15 15 15 15


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y231+3465x216y15+630x220y11