Characteristics of invariant weights related to code equivalence over rings

Autor: Marcus Greferath, Cathy Mc Fadden, Jens Zumbrägel
Přispěvatelé: Saadi, Assia
Rok vydání: 2012
Předmět:
FOS: Computer and information sciences
Ring-Linear Codes
Monomial
Picard–Lindelöf theorem
Computer Science - Information Theory
0102 computer and information sciences
01 natural sciences
94B05
11T71
05E99
Combinatorics
[MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT]
Weights
Compactness theorem
FOS: Mathematics
Danskin's theorem
0101 mathematics
Invariant (mathematics)
Brouwer fixed-point theorem
MacWilliams' Equivalence Theorem
[INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR]
Mathematics
Discrete mathematics
Information Theory (cs.IT)
Applied Mathematics
010102 general mathematics
Mathematics - Rings and Algebras
Extension Theorem
16. Peace & justice
Linear code
Computer Science Applications
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Finite field
Rings and Algebras (math.RA)
010201 computation theory & mathematics
[INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT]
Zdroj: Designs, Codes and Cryptography. 66:145-156
ISSN: 1573-7586
0925-1022
DOI: 10.1007/s10623-012-9671-9
Popis: 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].
11 pages
Databáze: OpenAIRE
Externí odkaz: