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Electronic Journal of Combinatorics
Article . 2002 . Peer-reviewed
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Electronic Journal of Combinatorics
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https://dx.doi.org/10.37236/16...
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MacWilliams Identities and Matroid Polynomials

MacWilliams identities and matroid polynomials
descriptionPublicationkeyboard_double_arrow_right Article 22 Apr 2002Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 9 (eissn: 1077-8926, Copyright policy )
Authors: Thomas Britz;

doi: 10.37236/1636

MacWilliams Identities and Matroid Polynomials

Abstract

We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the $r$th support weight enumerators of the code. One of our main tools is a generalisation of a decomposition theorem due to Brylawski.

Related Organizations
Keywords

linear code, Combinatorial aspects of matroids and geometric lattices, Linear codes (general theory), weight enumerator

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    selected citations
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    		 11
    popularity
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    		 Average
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
11
Average
Top 10%
Average
gold
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