The MacWilliams identity for m-spotty Rosenbloom–Tsfasman weight enumerator

Abstract

The communication systems and disk or tape memory can sometimes cause clusters of errors, namely burst errors. There have been many designs in order to detect and even correct such errors. Recently, a new class of codes called m-spotty byte error correcting codes has found applications in high speed memory systems that employ random access memory chips wide Input/Output data, especially at 8, 16, or 32bits. The MacWilliams identity provides the relationship between the weight distribution of a code and that of its dual code. Also, an interesting new metric called Rosenbloom–Tsfasman metric has been studied as an alternative metric for linear codes recently. In this paper, we combine these two interesting topics and introduce the m-spotty Rosenbloom–Tsfasman weights and the m-spotty Rosenbloom–Tsfasman weight enumerator of a binary code. Moreover, we prove a MacWilliams identity for the m-spotty Rosenbloom–Tsfasman weight enumerators.