MacWilliams identities and matroid polynomials
type: Item
instance of: scholarly article
title: MacWilliams identities and matroid polynomials
zbMATH Open document ID: 1038.05008
author: Thomas Britz
published in: The Electronic Journal of Combinatorics
publication date: 2002-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/123544
full work available at URL: v9i1r19.html
review text: In 1963, MacWilliams proved an identity linking the weight enumerators of a linear code and its dual. In 1976, Greene showed that the weight enumerator of a linear code could be expressed in terms of the Tutte polynomial of the matroid that is represented by a generator matrix of the code. Using this fact, Greene was able to reprove the identity of MacWilliams. This paper proves several generalizations of the MacWilliams identity including results that extend earlier generalizations due to Kløve and Shiromoto. In addition, the theorem of Greene and an extension of it due to Barg are also generalized. An important tool in these last two proofs is an extension of Brylawski's characterization of the Tutte polynomial.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1741005
zbMATH Keywords: linear code
zbMATH Keywords: weight enumerator
reviewed by: James Oxley
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1741005