Improved decoding of symmetric rank metric errors

12/16/2022

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by   Alain Couvreur, et al.

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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 correcting symmetric errors of rank up to n-k. The two mentioned decoders are deterministic and worst case.