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

Abstract

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 O max{n 3 , n 2 s} operations in Fqm , 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.