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Characteristics of Invariant Weights Related to Code Equivalence over Rings

Cathy Mc Fadden 1 Marcus Greferath 1 Jens Zumbragel 1 
1 School of Mathematical Sciences [Dublin]
Abstract : The Extension Theorem states that, for a given weight on he alphabet, every linear isometry between linear codes extends to a mono- mial transformation of the entire space. This theorem has been proved for several weights and alphabets, including the original MacWilliams' Equivalence Theorem for Hamming weight on codes over nite elds. Now we ask: What conditions must a weight satisfy so that the Extension Theorem will hold? In this paper we provide an algebraic framework for determining such conditions, generalising the approach taken in [5].
Keywords : Ring-Linear Codes MacWilliams' Equivalence Theorem Extension Theorem Weights Ring-Linear Codes.
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https://hal.inria.fr/inria-00607730
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Submitted on : Monday, July 11, 2011 - 10:13:17 AM
Last modification on : Wednesday, November 29, 2017 - 10:27:36 AM
Long-term archiving on: : Monday, November 12, 2012 - 10:40:17 AM

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  • HAL Id : inria-00607730, version 1

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Cathy Mc Fadden, Marcus Greferath, Jens Zumbragel. Characteristics of Invariant Weights Related to Code Equivalence over Rings. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.91-100. ⟨inria-00607730⟩

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