Characteristics of invariant weights related to code equivalence over rings

Marcus Greferath, Cathy Mc Fadden, Jens Zumbrägel

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

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).
Original languageUndefined/Unknown
Pages (from-to)145-156
Number of pages12
JournalDESIGNS CODES AND CRYPTOGRAPHY
Volume66
Issue number1-3
DOIs
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • MacWilliams’ equivalence theorem
  • extension theorem
  • weights
  • ring-linear codes

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