On Decoding High-Order Interleaved Sum-Rank-Metric Codes

03/30/2023

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by   Thomas Jerkovits, et al.

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We consider decoding of vertically homogeneous interleaved sum-rank-metric codes with high interleaving order s, that are constructed by stacking s codewords of a single constituent code. We propose a Metzner–Kapturowski-like decoding algorithm that can correct errors of sum-rank weight t <= d-2, where d is the minimum distance of the code, if the interleaving order s > t and the error matrix fulfills a certain rank condition. The proposed decoding algorithm generalizes the Metzner–Kapturowski(-like) decoders in the Hamming metric and the rank metric and has a computational complexity of Õ(max(n^3, n^2 s)) operations in 𝔽_q^m, where n is the length of the code. The scheme performs linear-algebraic operations only and thus works for any interleaved linear sum-rank-metric code. We show how the decoder can be used to decode high-order interleaved codes in the skew metric. Apart from error control, the proposed decoder allows to determine the security level of code-based cryptosystems based on interleaved sum-rank metric codes.