An algebraic characterization of q-ary images of qn-ary codes invariant under a permutation

This paper introduces for the first time a characterization of the q-ary images of qⁿ-ary σ-codes, i.e. linear codes of length m over F_qⁿ that are invariant under the action of a permutation σ, in the special case when F_qⁿ = F_q(β) = F_q(β^l) for some l > 0, β ϵ F_qⁿ. This is achieved by introducing an appropriate module structure on F_q^nm.