Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.-Reference-Cited by-同舟云学术

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Published:2021-06-01 Issue:2 Volume:29 Page:25-50
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Castillo-Guillén C. A.¹,Álvarez-García C.²

Affiliation:

1. Department of Mathematics , Universidades para el Bienestar Benito Juárez García , Tláhuac Ave 6391, 13360 , México City , México

2. Department of Mathematics , Universidad Autónoma Metropolitana-I , San Rafael Atlixco Ave 186, 09340 , México City , México

Abstract

Abstract Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2021-0017

Reference17 articles.

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2. [2] C. A. Castillo-Guillén, C. Rentería-Márquez, H. Tapia-Recillas, Consta-cyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, Finite Fields Appl. 43 1-21 (2017)

3. [3] C. A. Castillo-Guillén, C. Rentería-Márquez, H. Tapia-Recillas, Duals of constacyclic codes over finite local Frobenius non-chain rings of length 4, Discrete Math. 341 919-933 (2018)

4. [4] C. A. Castillo-Guillén, C. Rentería-Márquez, E. Sarmiento-Rosales, H. Tapia-Recillas, R. H. Villareal, The dual of a constacyclic code, self dual and reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings of nilpotency index 3, Discrete Math. 342 2283-2296 (2019)

5. [5] C. A. Castillo-Guillén, C. Rentería-Márquez, Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4, An. Stiint. Univ. Ovidius Constanta Ser. Mat. (to appear)