Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4-Reference-Cited by-同舟云学术

Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Published:2020-07-01 Issue:2 Volume:28 Page:67-91
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Castillo-Guillén C. A.¹,Rentería-Márquez C.²

Affiliation:

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

2. Department of Mathematics, Escuela Superior de Física y Matemáticas , Instituto Politécnico Nacional, Instituto Politécnico Nacional Ave s/n, 07300 , Ciudad de México, México

Abstract

Abstract The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p 5 elements (p a prime) and nilpotency index 4 are given. And the number and structure of γ-constacyclic codes over those rings, of length relatively prime to the characteristic of the residue field of the ring, are determined.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2020-0020

Reference11 articles.

1. [1] Y. Cao, Yonglin Cao, Negacyclic codes over the local ring 𝕑4[v]/ 〈v2 + 2v〉 of oddly even length and their Gray images, Finite Fields Appl. 52 (2018) 67-93.10.1016/j.ffa.2018.03.005

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 (2017) 1-21.10.1016/j.ffa.2016.08.004

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 (2018) 919-933.10.1016/j.disc.2017.12.014

4. [4] H. Q. Dinh, S. R. López-Permouth, Cyclic and Negacyclic Codes Over Finite Chain Rings, IEEE Trans. Inf. Theory 50 (2004) 1728-1744.10.1109/TIT.2004.831789

5. [5] H. Q. Dinh, A. K. Singh, P. Kumar, S. Sriboonchitta, On the structure of cyclic codes over the ring 𝕑2s [u]/ 〈 uk〉, Discrete Math. 341 (2018) 2243-2275.10.1016/j.disc.2018.04.028

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4;Analele Universitatii "Ovidius" Constanta - Seria Matematica;2022-02-01