Code details

best found code with parameters
q=3 k=7 n=243
minimum distance = 156

this is new code


the previous bounds were 154/159
this is a projective code


We used the prescribed group of automorphisms with the following generators


2 0 0 0 0 0 0
0 0 0 2 0 0 0
0 2 0 0 0 0 0
0 0 2 0 0 0 0
0 0 0 0 0 0 2
0 0 0 0 2 0 0
0 0 0 0 0 2 0

2 0 0 0 0 0 0
0 2 0 0 0 0 0
0 0 2 0 0 0 0
0 0 0 0 2 0 0
0 0 0 2 0 0 0
0 0 0 0 0 0 2
0 0 0 0 0 2 0

This group make 59 orbits of sizes:

6 15 10 15 6 1 6 1 6 15 10 15 6 1 6 15 10 15 6 1 6 30 15 10 30 30 10 30 30 15 30 30 60 30 10 15 30 15 30 30 30 30 30 30 6 10 15 30 10 30 30 30 30 30 15 30 30 15 10


The solution of the corresponding linear system of equations was found after less than 6143 seconds:

0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 87 81 81 78 81 54 69 87 87 78 75 87 78 78 63 81 84 72 72 87 87 78 87 72 72 78 84 84 87 84 87 87 81 87 81 78 75 87 87 84 81 63 81 78 87 81 87 87 63 84 81 87 87 84 87 81 66 87 72


This produces the following generator matrix

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 2 2 2 0 0 0 2 2 2 2 2 2 2 1 1 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 2 2 0 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 2 2 1 1 1 0 0 2 2 1 1 1 1 1 1 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 0 0 2 2 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 2 2 2 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 0 0 0 0 0 0 2 2 1 1 0 0 0 2 2 0 0 2 2 2 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1
0 2 0 2 2 0 2 2 0 0 2 2 2 2 1 2 1 0 0 0 0 2 2 2 0 0 0 2 0 0 0 2 0 2 2 0 2 2 2 2 2 2 2 1 2 2 2 1 2 1 1 2 1 1 2 2 1 1 2 1 1 1 1 2 1 2 1 1 2 1 0 1 0 2 1 1 1 1 2 1 1 0 2 1 1 1 1 0 0 2 2 2 2 2 1 0 1 0 2 1 1 1 1 0 1 0 1 1 0 2 1 1 1 1 0 1 1 0 0 0 0 2 2 0 1 0 1 1 0 1 1 0 0 0 0 0 2 2 1 0 0 2 2 1 1 0 2 2 0 0 2 2 1 1 0 0 0 0 0 2 2 0 0 2 2 0 0 2 0 0 2 0 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 2 1 1 0 1 0 0 2 1 0 0 0 2 2 2 0 0 0 2 2 1 1 1 1 0 0 0 2 2 1 1 1 1 0 0 0 0 0 0
2 0 2 0 2 2 0 2 0 0 2 2 2 1 2 2 1 0 0 2 2 0 0 2 0 0 2 0 0 0 2 0 0 2 2 2 0 2 2 2 2 2 1 2 2 2 1 2 1 2 1 1 2 1 2 2 1 1 1 2 1 1 1 1 2 1 2 1 1 2 1 0 1 1 0 2 1 1 1 2 1 1 1 0 2 1 1 2 2 0 0 2 2 1 2 1 0 1 1 0 2 1 1 1 0 1 0 1 1 1 0 2 1 1 1 0 1 0 0 2 2 0 0 1 0 1 0 1 1 0 1 0 0 2 2 1 0 0 0 2 1 0 1 0 2 2 0 2 2 1 0 1 0 2 0 0 0 0 2 0 2 0 0 2 2 0 2 0 0 2 0 2 0 1 2 1 1 2 1 1 2 2 1 2 2 1 1 1 1 0 0 0 2 1 1 0 0 0 0 0 0 2 1 1 0 0 0 1 0 2 1 0 0 2 2 2 0 0 0 2 1 1 0 1 0 0 2 1 2 1 1 0 1 0 0 2 1 0 0 0 0 0 0
2 2 2 0 0 0 2 0 0 2 2 2 1 2 2 2 1 0 2 0 2 0 2 0 0 2 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 1 2 2 2 2 1 1 1 2 2 2 1 2 2 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 2 0 0 2 2 1 2 2 0 1 1 0 2 2 1 2 1 0 1 1 1 1 1 1 1 2 0 0 2 1 1 1 0 0 2 0 1 1 0 2 0 1 0 2 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 2 1 2 2 1 2 1 2 0 0 0 0 2 0 0 0 0 1 0 2 0 0 1 0 2 0 2 0 0 2 0 2 2 0 2 2 2 0 0 0 1 1 2 1 1 2 1 2 1 2 0 1 0 0 2 1 2 1 1 0 0 0 1 2 1 2 1 1 1 2 1 0 0 0 0 0 0 0 0 0 2 1 1 2 1 1 1 2 1 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 1 0 0 2 1
2 2 0 2 0 2 0 0 2 0 2 1 2 2 2 2 1 0 2 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 0 2 1 2 2 2 2 2 1 1 2 1 2 1 2 2 1 2 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 0 1 1 2 0 1 2 2 1 1 2 0 2 0 1 2 1 2 1 0 1 1 1 1 2 0 1 1 2 0 1 1 0 1 0 1 1 2 0 2 0 1 0 0 1 2 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 2 2 1 2 2 0 0 1 0 2 0 0 2 0 1 2 0 0 0 0 1 0 2 0 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0 1 1 1 2 1 1 2 1 2 2 1 0 2 1 0 0 1 2 1 1 2 1 0 0 0 1 2 1 0 0 0 1 2 1 0 0 0 0 0 0 1 2 1 1 2 1 0 0 0 1 0 2 1 0 0 1 2 1 0 0 0 0 0 0 1 0 2 1 0 0



Which is a code with the following weight distribution
1y243+712x156y87+310x159y84+492x162y81+284x165y78+80x168y75+142x171y72+12x174y69+60x177y66+92x180y63+2x189y54