Characteristics of Invariant Weights Related to Code Equivalence over Rings

Details Characteristics of Invariant Weights Related to Code Equivalence over Rings Characteristics of Invariant Weights Related to Code Equivalence over Rings

2011-10-07

arxiv.org/abs/1110.1538v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

The Equivalence Theorem states that, for a given weight on the alphabet, every linear 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, Honold '06].

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