List Decoding of Lee Metric Codes
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چکیده
1 Abbreviations and Notations 2
منابع مشابه
Decoding of Block and Convolutional Codes in Rank Metric DISSERTATION
Rank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowadays...
متن کاملDecoding of block and convolutional codes in rank metric
R ank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowaday...
متن کاملA new class of rank-metric codes and their list decoding beyond the unique decoding radius
Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. The evidences to support this view include: (i) so far people have not found polynomial time list decoding algorithms of rank-metric codes with decoding radius beyond (1 − R)/2 (where R is the rate of code) if ratio of the number of rows over the number of columns is constant, but not very sm...
متن کاملOn the List Decodability of Self-orthogonal Rank Metric Codes
V. Guruswami and N. Resch prove that the list decodability of Fq-linear rank metric codes is as good as that of random rank metric codes in [17]. Due to the potential applications of self-orthogonal rank metric codes, we focus on list decoding of them. In this paper, we prove that with high probability, an Fq-linear self-orthogonal rank metric code over Fn×m q of rate R = (1 − τ)(1 − n mτ) − is...
متن کاملEvading Subspaces Over Large Fields and Explicit List-decodable Rank-metric Codes
We construct an explicit family of linear rank-metric codes over any field Fh that enables efficient list decoding up to a fraction ρ of errors in the rank metric with a rate of 1−ρ−ε, for any desired ρ ∈ (0, 1) and ε > 0. Previously, a Monte Carlo construction of such codes was known, but this is in fact the first explicit construction of positive rate rank-metric codes for list decoding beyon...
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تاریخ انتشار 2011