Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric

We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes the rank metric, lifted subspace and linearized Reed-Solomon sum-rank metric. The speed-ups are achieved by new that reduce cores of underlying computational problems decoders to one common tool: computing left right approximant bases matrices over skew polynomial rings. To accomplish this, we describe a skew-analogue PM-Basis algorithm ordinary polynomials. This captures bulk work multiplication polynomials, complexity benefit comes from performing this faster than classical quadratic complexity. various decoding-related interesting their own have further applications, particular parts several other foundational related remainder-evaluation