Interpolation-based decoding of folded variants of linearized and skew Reed–Solomon codes

• DOI: 10.1007/s10623-023-01214-8
• Publication Date: 2023-05-06T05:01:56Z
• Authors: Felicitas Hörmann; Hannes Bartz
• Keywords: List decoding; Reed–Solomon error correction

Abstract The sum-rank metric is a hybrid between the Hamming and rank suitable for error correction in multishot network coding distributed storage as well design of quantum-resistant cryptosystems. In this work, we consider construction decoding folded linearized Reed–Solomon (FLRS) codes, which are shown to be maximum distance (MSRD) appropriate parameter choices. We derive an efficient interpolation-based algorithm FLRS codes that can used list decoder or probabilistic unique decoder. proposed scheme correct errors beyond radius with computational complexity quadratic length unfolded code. show how error-correction capability optimized high-rate by alternative choice interpolation points. heuristic upper bound on failure probability verify its tightness Monte Carlo simulations. Further, study skew Reed-Solomon metric. Up our knowledge, first MSRD different block sizes come along algorithm.