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Linear Algebra and its Applications
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The weight distribution of codes over finite chain rings

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2023Embargo end date: 01 Jan 2022 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 675, pages 90-105 (issn: 0024-3795, Copyright policy )
Authors: Cavicchioni G.; Meneghetti A.;

doi: 10.1016/j.laa.2023.06.015 , 10.48550/arxiv.2210.15436

arXiv: 2210.15436

handle: 11572/384211

The weight distribution of codes over finite chain rings

Abstract

In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code. Thanks to these relations we are able to compute the full weight distribution of codes with small Singleton defects, such as MDS, MDR and AMDR codes.

Related Organizations
Keywords

FOS: Computer and information sciences, ring-linear code, Computer Science - Information Theory, Information Theory (cs.IT), Ring-linear code; Weight distribution, weight distribution, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Finite commutative rings, FOS: Mathematics, 94B05, 13M99, Linear codes (general theory)

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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!
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