A MACMILLIAMS TYPE IDENTITY FOR M-SPOTTY GENERALIZED LEE WEIGHT ENUMERATORS OVER ZQ

Year 2013, Volume: 1 Issue: 1, 111 - 116, 01.06.2013

Vedat Şiap

Abstract

Burst errors are very common in practice. There have been manydesigns in order to control and correct such errors.Recently, a new classof byte error control codes called spotty byte error control codes has beenspecifically designed to fit the large capacity memory systems that use highdensity random access memory (RAM) chips with input/output data of 8, 16,and 32 bits. The MacWilliams identity describes how the weight enumeratorof a linear code and the weight enumerator of its dual code are related. Also,Lee metric which has attracted many researchers due to its applications. Inthis paper, we combine these two interesting topics and introduce the m-spottygeneralized Lee weights and the m-spotty generalized Lee weight enumeratorsof a code over Zqand prove a MacWilliams type identity. This generalizationincludes both the case of the identity given in the paper [I. Siap, MacWilliamsidentity for m-spotty Lee weight enumerators, Appl.Math.Lett.23 (1)(2010) 13-16] and the identity given in the paper [M. ¨Ozen, V. S¸iap, TheMacWilliams identity for m-spotty weight enumerators of linear codes overfinite fields, Comput. Math. Appl. 61 (4) (2011) 1000-1004] over Z2and Z3as special cases

Keywords

MacWilliams identity, weight enumerator, m-spotty weight

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