# Article ID: MTJPAM-D-21-00073

## Title: Bounds on the covering radius of some classes code, simplex code and MacDonald code in R

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00073; Volume 4 / Issue 2 / Year 2022, Pages 37-44

Document Type: Research Paper

Author(s): Panchanathan Chella Pandian a

Received: 3 December 2021, Accepted: 2 June 2022, Published: 14 July 2022.

Corresponding Author: Panchanathan Chella Pandian (Email address: chellapandianpc@gmail.com; chella@andavancollege.ac.in)

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Abstract

In this paper, study of the codes in $R ={\mathbb Z_2}\mathbb R,$ where $\mathbb R={\mathbb Z_2+u\mathbb Z_2}$, $u^2=0.$ Its related parameter of codes over $R ={\mathbb Z_2}\mathbb R,$ with different distance are discussed. The block repetition codes over $R$ are defined and the covering radius for block repetition codes, simplex code and macdonald code of type $\alpha$ and type $\beta$ in $R$ are obtained.

Keywords: Code, finite ring, additive codes, parameter, different distance, block repetition code, simplex code, Macdonald code

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