Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(3): 809-823

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.809

Copyright © The Korean Mathematical Society.

An identity between the $m$-spotty Rosenbloom-Tsfasman weight enumerators over finite commutative Frobenius rings

Mehmet \"{O}zen, Minjia Shi, and Vedat \c{S}iap

Sakarya University, Anhui University, Yildiz Technical University

Abstract

This paper is devoted to presenting a MacWilliams type identity for $m$-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the $m$-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.

Keywords: byte error-control codes, $m$-spotty byte error, MacWilliams identity, weight enumerators

MSC numbers: 94A15, 94B20, 94B60