MacWilliams Identity for M-Spotty Weight Enumerator

Kazuyoshi SUZUKI

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.2    pp.526-531
Publication Date: 2010/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.526
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
MacWilliams identity,  weight enumerator,  m-spotty weight,  m-spotty byte error,  t/b-error,  

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M-spotty byte error control codes are very effective for correcting/detecting errors in semiconductor memory systems that employ recent high-density RAM chips with wide I/O data (e.g., 8, 16, or 32 bits). In this case, the width of the I/O data is one byte. A spotty byte error is defined as random t-bit errors within a byte of length b bits, where 1 ≤ tb. Then, an error is called an m-spotty byte error if at least one spotty byte error is present in a byte. M-spotty byte error control codes are characterized by the m-spotty distance, which includes the Hamming distance as a special case for t = 1 or t = b. The MacWilliams identity provides the relationship between the weight distribution of a code and that of its dual code. The present paper presents the MacWilliams identity for the m-spotty weight enumerator of m-spotty byte error control codes. In addition, the present paper clarifies that the indicated identity includes the MacWilliams identity for the Hamming weight enumerator as a special case.

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