MacWilliams Identities for $m$-tuple Weight Enumerators
نویسندگان
چکیده
منابع مشابه
MacWilliams Identities for $m$-tuple Weight Enumerators
Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of m-tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kløve, Shiromoto, Wan, and others. W...
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Codes over various metrics such as Rosenbloom-Tsfasman (RT), Lee, etc. have been considered. Recently, codes over poset metrics have been studied. Poset metric is a great generalization of many metrics especially the well-known ones such as the RT and the Hamming metrics. Poset metric can be realized on the channels with localized error occurrences. It has been shown that MacWilliams identities...
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Computer memory systems using high-density RAM chips are vulnerable to m-spotty byte errors when they are exposed to high-energy particles. These errors can be effectively detected or corrected using (m-spotty) byte error-control codes. In order to study the properties of these codes and to measure their error-detection and error-correction performance, m-spotty weight enumerators are introduce...
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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 errorcontrol codes. The MacWilliams identity provides the relationship between the weight distribution of a code and...
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The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. M. Özen and V. Siap [7] proved a MacWilliams identity for the m-spotty Rosenbloom-Tsfasman (shortly RT) weight enumerator...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/120876356