Degenerate flag varieties in network coding

03/04/2020

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by   Ghislain Fourier, et al.

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RWTH Aachen University

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Building upon the application of flags to network coding introduced by Liebhold, Nebe, and Vazquez-Castro, we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to the space of upper triangular matrices endowed with the flag rank metric. This suggests the development of a theory for flag rank metric codes in analogy to the rank metric codes used in linear subspace coding.