On the structure of 1-generator quasi-polycyclic codes over finite chain rings

11/09/2021

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by   Rongsheng Wu, et al.

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Quasi-polycyclic (QP for short) codes over a finite chain ring R are a generalization of quasi-cyclic codes, and these codes can be viewed as an R[x]-submodule of ℛ_m^ℓ, where ℛ_m:= R[x]/⟨ f⟩, and f is a monic polynomial of degree m over R. If f factors uniquely into monic and coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials and the minimal generating sets of 1-generator QP codes as R-modules. In addition, we also determine the parity check polynomials for these codes by using the strong Gröbner bases. In particular, via Magma system, some quaternary codes with new parameters are derived from these 1-generator QP codes.