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MDS and self-dual codes over rings

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2012Embargo end date: 01 Jul 2012 English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 18, pages 1,061-1,075 (issn: 1071-5797, Copyright policy )
Authors: Kenza Guenda; T. Aaron Gulliver;

doi: 10.1016/j.ffa.2012.09.003 , 10.48550/arxiv.1207.3384

arXiv: 1207.3384

MDS and self-dual codes over rings

Abstract

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.

Related Organizations
Keywords

formal power series rings, constacyclic codes, FOS: Computer and information sciences, cyclic codes, Algebra and Number Theory, Applied Mathematics, Computer Science - Information Theory, Information Theory (cs.IT), Formal power series rings, Codes over rings, Theoretical Computer Science, Finite chain rings, Bounds on codes, finite chain rings, self-dual codes, codes over rings, MDS codes, Cyclic codes, Principal ideal rings, Engineering(all), Linear codes (general theory)

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    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.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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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!
23
Top 10%
Top 10%
Top 10%
Green
hybrid