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Rank subcodes in multicomponent network coding

  • Coding Theory
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Abstract

A new class of subcodes in rank metric is proposed; based on it, multicomponent network codes are constructed. Basic properties of subspace subcodes are considered for the family of rank codes with maximum rank distance (MRD codes). It is shown that nonuniformly restricted rank subcodes reach the Singleton bound in a number of cases. For the construction of multicomponent codes, balanced incomplete block designs and matrices in row-reduced echelon form are used. A decoding algorithm for these network codes is proposed. Examples of codes with seven and thirteen components are given.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    E. M. Gabidulin & N. I. Pilipchuk

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  1. E. M. Gabidulin
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  2. N. I. Pilipchuk
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Correspondence to E. M. Gabidulin.

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Original Russian Text © E.M. Gabidulin, N.I. Pilipchuk, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 1, pp. 46–60.

Supported in part by the Russian Foundation for Basic Research, project no. 12-07-00122-a.

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Gabidulin, E.M., Pilipchuk, N.I. Rank subcodes in multicomponent network coding. Probl Inf Transm 49, 40–53 (2013). https://doi.org/10.1134/S0032946013010043

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