Decoding High-Order Interleaved Rank-Metric Codes

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh

Abstract: This paper presents an algorithm for decoding any linear interleaved code of high interleaving order in the rank metric. The new decoder is an adaptation of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to correct all rank errors of weight up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d-2$</tex> whose rank over the large base field of the code equals the number of errors, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex> is the minimum rank distance of the underlying code. It is based on linear-algebraic computations, and has an explicit and easy-to-handle success condition.