Improved decoding of symmetric rank metric errors

We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be corrected. Moreover, the corresponding family of...

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Bibliographic Details
Main Author Couvreur, Alain
Format Journal Article
LanguageEnglish
Published 16.12.2022
Subjects
Computer Science - Information Theory
Mathematics - Information Theory
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Summary:We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be corrected. Moreover, the corresponding family of decodable codes includes Gabidulin codes of rate $<1/2$. Second, for rates $>1/2$, we propose a decoder for Gabidulin codes correcting symmetric errors of rank up to $n-k$. The two mentioned decoders are deterministic and worst case.
DOI:10.48550/arxiv.2212.08713