
A Decoding Algorithm for Rank Metric Codes
In this work we will present algorithms for decoding rank metric codes. ...
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Residues of skew rational functions and linearized Goppa codes
This paper constitutes a first attempt to do analysis with skew polynomi...
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On the hardness of code equivalence problems in rank metric
In recent years, the notion of rank metric in the context of coding theo...
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Generic Decoding in the SumRank Metric
We propose the first nontrivial generic decoding algorithm for codes in...
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On Skew Convolutional and Trellis Codes
Two new classes of skew codes over a finite field are proposed, called ...
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SumRank BCH Codes and CyclicSkewCyclic Codes
In this work, cyclicskewcyclic codes and sumrank BCH codes are introd...
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An AssmusMattson Theorem for Rank Metric Codes
A t(n,d,λ) design over F_q, or a subspace design, is a collection of d...
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Fast Decoding of Codes in the Rank, Subspace, and SumRank Metric
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized ReedSolomon codes in the sumrank metric. The speedups are achieved by new algorithms that reduce the cores of the underlying computational problems of the decoders to one common tool: computing left and right approximant bases of matrices over skew polynomial rings. To accomplish this, we describe a skewanalogue of the existing PMBasis algorithm for matrices over ordinary polynomials. This captures the bulk of the work in multiplication of skew polynomials, and the complexity benefit comes from existing algorithms performing this faster than in classical quadratic complexity. The new algorithms for the various decodingrelated computational problems are interesting in their own and have further applications, in particular parts of decoders of several other codes and foundational problems related to the remainderevaluation of skew polynomials.
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