The MacWilliams identity for m-spotty weight enumerators of linear codes over finite fields

Abstract

Some of the error control codes are applied to high speed memory systems using RAM chips with either 1-bit I/O data ( b = 1 ) or 4-bit I/O data ( b = 4 ) . However, modern large-capacity memory systems use RAM chips with 8, 16, or 32 bits of I/O data. A new class of codes called m -spotty byte error codes provides a good source for correcting/detecting errors in those memory systems that use high-density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). The MacWilliams identity provides the relation of weight distribution of a code and that of its dual code. The main purpose of this paper is to present a version of the MacWilliams identity for m -spotty weight enumerators of linear codes over arbitrary finite fields.