A connection between sumsets and covering codes of a module

Otávio J. N. T. N. dos Santos; Emerson L. Monte Carmelo

doi:10.3934/amc.2018035

Article Contents

2018, Volume 12, Issue 3: 595-605. Doi: 10.3934/amc.2018035

This issue Previous Article Parameters of LCD BCH codes with two lengths Next Article On self-orthogonal designs and codes related to Held's simple group

A connection between sumsets and covering codes of a module

Otávio J. N. T. N. dos Santos^1, and
Emerson L. Monte Carmelo^2, ,

1.
Universidade Estadual de Mato Grosso do Sul, Unidade de Ponta Porã, Rua Itiberé Vieira, S/N, Ponta Porã-MS, CEP 79907-414, Brazil
2.
Universidade Estadual de Maringá, Departamento de Matemática, Av. Colombo, 5790 - Campus Universitário, Maringá-PR, CEP 87020-900, Brazil

^* Corresponding author: elmcarmelo@uem.br
^* Corresponding author: elmcarmelo@uem.br

Received: September 30, 2017

Published: July 2018

The first author is partially supported by FUNDECT/CNPq grant 054/2015
The second author is partially supported by CNPq/MCT grant 311793/2016-0.

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Abstract

In this work we focus on a connection between sumsets and covering codes in an arbitrary finite module. For this purpose, bounds on a new problem on sumsets are obtained from well-known results of additive number theory, namely, the Cauchy-Davenport theorem, the Vosper theorem and a theorem due to Hamidoune-Rødseth. As an application, the approach is able to extend the Blokhuis-Lam theorems and a construction of covering codes by Honkala to an arbitrary module.

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Mathematics Subject Classification: Primary: 11T71; Secondary: 11P70, 13M99, 94B75.

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References

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