Degenerate flag varieties in network coding

DOI10.3934/amc.2021027zbMath1522.94134arXiv2003.02002OpenAlexW3178208664MaRDI QIDQ6167303

Ghislain Fourier, Gabriele Nebe

Publication date: 7 July 2023

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.02002

zbMATH Keywords

upper triangular matriceserror correcting codesnetwork codingdegenerate flag varietyGrassmann distance on flagsflag rank metric codes

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Homogeneous spaces and generalizations (14M17) Group actions on varieties or schemes (quotients) (14L30) Theory of error-correcting codes and error-detecting codes (94B99)

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Cites Work

• Rank-metric codes and their duality theory
• \({\mathbb{G}_a^M}\) degeneration of flag varieties
• PBW filtration and bases for irreducible modules in type \({\text{\textsf{A}}}_{n}\)
• Network coding with flags
• Linear degenerations of flag varieties
• Degenerate Flag Varieties of Type A and C are Schubert Varieties
• Coding for Errors and Erasures in Random Network Coding
• A Rank-Metric Approach to Error Control in Random Network Coding

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