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An Unified Approach on Constructing of MDS Self-dual Codes via Reed-Solomon Codes

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arxiv 1905.06513 v1 pith:ICZ7YXHN submitted 2019-05-16 cs.IT math.IT

Aixian Zhang , Keqin Feng This is my paper · ORCID
classification cs.ITmath.IT
keywords codesself-dualreed-solomonapproachciteconstructionsgeneralizedresults
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Based on the fundamental results on MDS self-dual codes over finite fields constructed via generalized Reed-Solomon codes \cite{JX} and extended generalized Reed-Solomon codes \cite{Yan}, many series of MDS self-dual codes with different length have been obtained recently by a variety of constructions and individual computations. In this paper, we present an unified approach to get several previous results with concise statements and simplified proofs, and some new constructions on MDS self-dual codes. In the conclusion section we raise two open problems.

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  1. On Euclidean Hulls of MDS Codes

    cs.IT 2019-08 accept novelty 6.0 of 10

    Any self-orthogonal (extended) GRS code of dimension m yields MDS codes of every smaller dimension k with any Euclidean hull dimension from 0 to k.

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