Code details

best found code with parameters
q=4 k=5 n=70
minimum distance = 50

this is new optimal code


the previous bounds were 49/50
this is a projective code


We used the prescribed group of automorphisms with the following generators


1 1 0 0 0
3 2 0 0 0
0 0 3 0 2
0 0 3 3 1
0 0 0 3 0

This group makes 13 orbits of sizes:

7 5 35 35 35 35 35 35 35 35 35 7 7


The solution of the corresponding linear system of equations was found after less than 10 seconds:

0 0 0 0 1 1 0 0 0 0 0 0 0 20 14 20 20 12 18 12 18 18 20 20 10 20


This produces the following generator matrix

0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3
0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3 0 1 1 2 2 3 3
3 0 3 0 3 0 3 1 0 1 0 1 0 1 3 0 3 0 3 0 3 1 0 1 0 1 0 1 3 0 3 0 3 0 3 0 1 1 3 3 2 2 0 3 3 2 2 1 1 0 1 1 3 3 2 2 0 3 3 2 2 1 1 0 1 1 3 3 2 2
2 0 2 2 0 2 0 3 3 0 0 3 3 0 2 0 2 2 0 2 0 3 3 0 0 3 3 0 2 0 2 2 0 2 0 2 1 3 1 3 0 2 3 0 3 1 2 1 2 2 1 3 1 3 0 2 3 0 3 1 2 1 2 2 1 3 1 3 0 2



Which is a code with the following weight distribution
1y70+462x50y20+315x52y18+15x56y14+210x58y12+21x60y10