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

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