MacWilliams Identities for $m$-tuple Weight Enumerators

Nathan Kaplan

doi:10.1137/120876356

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arXiv · 1205.1277

MacWilliams Identities for $m$-tuple Weight Enumerators

Nathan Kaplan

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Abstract

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 Kl{\o}ve, Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple weight enumerators.

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Nathan Kaplan. 2012-05-07. MacWilliams Identities for $m$-tuple Weight Enumerators. https://doi.org/10.1137/120876356

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