automorphism group (linear code) (original) (raw)

Let 𝔽q be the finite field with q elements. The groupℳn,q of n×n monomial matrices with entries in 𝔽qacts on the set ℭn,q of linear codes over 𝔽q of block length n via the monomial transform: let M=(Mi⁢j)i,j=1n∈ℳn,q and C∈ℭn,q and set

This definition looks quite complicated, but since M is , it really just means that CM is the linear code obtained from C by permuting its coordinates and then multiplying each coordinate with some nonzero element from 𝔽q.