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The MacWilliams identity for m-spotty weight enumerator over \mathbbF2+u\mathbbF2+⋯+um-1\mathbbF2

2013/07/06 by Minjia Shi, Shi, Minjia · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1307.2228

Research paper, under review since 18th October 2012. arXiv admin note: substantial text overlap with arXiv:1307.1786

arxiv created 2013/07/06 · openalex publication_date 2013/07/06 · arxiv updated 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Past few years have seen an extensive use of RAM chips with wide I/O data (e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an m-spotty byte error, which can be effectively detected or corrected using byte error-control codes. The MacWilliams identity provides the relationship between the weight distribution of a code and that of its dual. The main purpose of this paper is to present a version of the MacWilliams identity for m-spotty weight enumerators over \mathbbmF2+u\mathbbmF2+⋯+um-1\mathbbmF2 (shortly Ru, m, 2).

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