Code details

best found code with parameters
q=3 k=7 n=186
minimum distance = 118

this is new code


the previous bounds were 117/121
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 makes 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 10000 seconds:

0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 65 68 60 41 65 51 65 55 61 59 64 64 65 55 61 59 64 64 65 55 61 61 59 64 65 61 64 59 61 61 64 64 61 59 64 61 65 64 61 59 65 64 61 61 65 64 68 66 60 68 41 65 66 65 66 68 65 66 33


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y186+180x118y68+180x120y66+432x121y65+390x122y64+576x125y61+40x126y60+270x127y59+6x131y55+2x135y51+90x145y41+20x153y33