Degenerate flag varieties in network coding

Ghislain Fourier; Gabriele Nebe

doi:10.3934/amc.2021027

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2023, Volume 17, Issue 4: 888-899. Doi: 10.3934/amc.2021027

This issue Previous Article A new twofold Cornacchia-type algorithm and its applications Next Article New quantum codes from skew constacyclic codes

Degenerate flag varieties in network coding

Ghislain Fourier^1, and
Gabriele Nebe^1, ,

RWTH Aachen University, 52056 Aachen, Germany

^* Corresponding author: Gabriele Nebe
^* Corresponding author: Gabriele Nebe

Received: March 2021

Early access: July 2021

Published: August 2023

This is a contribution to Project-ID 286237555 - TRR 195 - by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)..

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Abstract

Building upon the application of flags to network coding introduced in [6], 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.

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Mathematics Subject Classification: Primary: 20E42, 94B99; Secondary: 20B30.

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References

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