Code details

best found code with parameters
q=23 k=3 n=146
minimum distance = 138

this is new optimal code


the previous bounds were -1/138
this is a projective code


We used the prescribed group of automorphisms with the following generators


10 0 0
0 8 0
0 0 4

This group makes 53 orbits of sizes:

1 1 11 11 1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11


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

1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 2 2 7 8 2 7 8 7 8 4 5 5 6 5 8 7 7 7 7 5 7 6 8 8 4 8 5 1 8 8 8 8 6 8 6 8 2 8 8 8 7 8 8 8 8 3 2 8 4 8 3 7 0


This produces the following generator matrix

0 0 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22
0 22 0 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 22 2 16 4 18 6 10 20 14 8 12 1 19 3 9 21 17 7 15 5 13 11 1 19 3 9 21 17 7 15 5 13 11 1 19 3 9 21 17 7 15 5 13 11 1 19 3 9 21 17 7 15 5 13 11 1 19 3 9 21 17 7 15 5 13 11 1 19 3 9 21 17 7 15 5 13 11
22 0 0 14 20 18 4 2 10 22 8 12 16 6 17 1 21 7 5 13 3 11 15 19 9 6 12 10 18 16 2 14 22 4 8 20 22 6 4 12 10 18 8 16 20 2 14 16 22 20 6 4 12 2 10 14 18 8 1 7 5 13 11 19 9 17 21 3 15 13 19 17 3 1 9 21 7 11 15 5 10 20 16 12 4 14 6 8 22 2 18 11 21 17 13 5 15 7 9 1 3 19 20 8 4 22 14 2 16 18 10 12 6 13 1 19 15 7 17 9 11 3 5 21 4 14 10 6 20 8 22 2 16 18 12 7 17 13 9 1 11 3 5 19 21 15



Which is a code with the following weight distribution
1y146+5324x138y8+2420x139y7+968x140y6+1210x141y5+726x142y4+484x143y3+550x144y2+242x145y1+242x146