Packing and Covering Properties of Rank Metric Codes

DOI10.1109/TIT.2008.928284zbMath1322.94121arXivcs/0701098MaRDI QIDQ3604842

Maximilien Gadouleau, Zhiyuan Yan

Publication date: 24 February 2009

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cs/0701098

Mathematics Subject Classification ID

Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75) Combinatorial aspects of packing and covering (05B40)

Related Items (18)

Multiple-rate error-correcting coding scheme ⋮ Rank-metric codes and their duality theory ⋮ Design of \(\mathcal{T}\)-\textit{direct} codes over \(\mathrm{GF}(2^N)\) with increased users ⋮ Covering Radius of Matrix Codes Endowed with the Rank Metric ⋮ Saturating systems and the rank-metric covering radius ⋮ Saturating linear sets of minimal rank ⋮ Asymptotic behaviour of codes in rank metric over finite fields ⋮ Construction of high rate \(\mathcal {T}\)-direct codes ⋮ Algebraic decoding of folded Gabidulin codes ⋮ Codes with the rank metric and matroids ⋮ Linear subspaces of symmetric tensors whose non-zero elements have at least a prescribed rank ⋮ Chains of subsemigroups ⋮ On deep holes of Gabidulin codes ⋮ On the list decodability of self-orthogonal rank-metric codes ⋮ Partition-balanced families of codes and asymptotic enumeration in coding theory ⋮ Application of \(\mathcal{T}\)-direct codes in multiple-rate codes ⋮ Some important results on 𝒯-Direct codes ⋮ Rank-Metric Codes and Their Applications

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