Title : ( $ \mathbb{Z}_{p^r}\mathbb{Z}_{p^s}\mathbb{Z}_{p^t} $-additive cyclic codes )
Authors: Razieh Molaei , Kazem Khashyarmanesh ,
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Abstract
Let p be a prime number and r, s, t be positive integers such that r ≤ s ≤ t. A Z^pr Z^ps Z^pt -additive code is a Z^pt -submodule of Z^αpr × Z^βps × Z^γpt, where α, β, γ are positive integers. In this paper, we study Zpr Zps Zpt -additive cyclic codes. In fact, we show that these codes can be identified as submodules of the ring R = Zpr [x]/xα − 1× Zps [x]/xβ − 1× Zpt [x]/xγ − 1. Furthermore, we determine the generator polynomials and minimum generating sets of this kind of codes. Moreover, we investigate their dual codes.
Keywords
, generator polynomials, minimum generating sets, dual code.
@article{paperid:1094042,
author = {Molaei, Razieh and Khashyarmanesh, Kazem},
title = {$ \mathbb{Z}_{p^r}\mathbb{Z}_{p^s}\mathbb{Z}_{p^t} $-additive cyclic codes},
journal = {Advances in Mathematics of Communications},
year = {2022},
month = {January},
issn = {1930-5346},
keywords = {generator polynomials; minimum generating
sets; dual code.},
}
%0 Journal Article
%T $ \mathbb{Z}_{p^r}\mathbb{Z}_{p^s}\mathbb{Z}_{p^t} $-additive cyclic codes
%A Molaei, Razieh
%A Khashyarmanesh, Kazem
%J Advances in Mathematics of Communications
%@ 1930-5346
%D 2022
