On $$\mathbb {Z}_2\mathbb {Z}_4$$-additive polycyclic codes and their Gray images

Wu, Rongsheng; Shi, Minjia

doi:10.1007/s10623-021-00917-0

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2021

2025

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Cited by 7 publications

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“…• It is well-known that C is a polycyclic code if ℓ = 1. The algebraic structures of polycyclic codes over finite chain rings with a new duality were presented in [2,10], and it is worthy to note that polycyclic codes over Galois rings and mixed alphabet Z 2 Z 4 were studied in [11] and [12], respectively;…”

Section: Introductionmentioning

confidence: 99%

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

Wu¹,

Shi²,

Solé³

2021

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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 ℓ m , 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.

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