Direction of Research About Fault Tolerance

Optimal 4x10 Code Matrix (min. Hamm dist = 5)

1 1 1 1 1 0 0 0 0 0
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

Proof ?
Design ?