Characteristics of invariant weights related to code equivalence over rings

The Equivalence Theorem states that, for a given weight on an alphabet, every isometry between linear codes extends to a monomial transformation of the entire space. This theorem has been proved for several weights and alphabets, including the original MacWilliams’ Equivalence Theorem for the Hammin...

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Vydáno v:Designs, codes, and cryptography Ročník 66; číslo 1-3; s. 145 - 156
Hlavní autoři: Greferath, Marcus, Mc Fadden, Cathy, Zumbrägel, Jens
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.01.2013
Témata:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
MacWilliams’ equivalence theorem
Weights
11T71
94B05
Ring-linear codes
Extension theorem
05E99
ISSN:0925-1022, 1573-7586
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Popis
Shrnutí:The Equivalence Theorem states that, for a given weight on an alphabet, every isometry between linear codes extends to a monomial transformation of the entire space. This theorem has been proved for several weights and alphabets, including the original MacWilliams’ Equivalence Theorem for the Hamming weight on codes over finite fields. The question remains: 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 Greferath and Honold (Proceedings of the Tenth International Workshop in Algebraic and Combinatorial Coding Theory (ACCT-10), pp. 106–111. Zvenigorod, Russia, 2006 ).
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-012-9671-9