Code details

best found code with parameters
q=8 k=5 n=130
minimum distance = 107

this is new code


the previous bounds were 106/111
this is a projective code


We used the prescribed group of automorphisms with the following generators


4 2 2 1 1
1 5 0 2 1
0 2 5 7 7
4 1 3 0 0
7 1 4 7 0

This group makes 81 orbits of sizes:

63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 9 63 63 63 21 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 21 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 3 63 21 3 3 1


The solution of the corresponding linear system of equations was found after less than 22 seconds:

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 1 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 1 0 0 0 0 0 0 1 0 0 0 0 1 13 18 5 13 17 23 22 15 11 13 17 15 13 11 15 15 17 21 15 17 17 15 7 13 17 13 13 19 23 19 17 15 23 13 21 17 13 17 22 11 17 17 15 15 14 15 23 13 17 17 14 23 11 15 17 19 23 19 15 22 9 19 14 19 14 15 21 19 15 17 18 17 15 18 17 19 19 22 3 2 18


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y130+2646x107y23+924x108y22+1323x109y21+3675x111y19+1386x112y18+7497x113y17+6027x115y15+1764x116y14+4410x117y13+1764x119y11+441x121y9+441x123y7+441x125y5+7x127y3+21x128y2