DeepAI AI Chat
Log In Sign Up

Degenerate flag varieties in network coding

03/04/2020
by   Ghislain Fourier, et al.
RWTH Aachen University
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/24/2023

Sum-rank metric codes

Sum-rank metric codes are a natural extension of both linear block codes...
01/29/2023

Rank Generalized Subsapce subcode

Rank metric codes were study by E. Gabidulin in 1985 after a brief intro...
06/01/2018

An Assmus-Mattson Theorem for Rank Metric Codes

A t-(n,d,λ) design over F_q, or a subspace design, is a collection of d...
11/15/2022

Divisible linear rank metric codes

A subspace of matrices over 𝔽_q^e^m× n can be naturally embedded as a su...
01/29/2019

Interleaving Loidreau's Rank-Metric Cryptosystem

We propose and analyze an interleaved variant of Loidreau's rank-metric ...
06/04/2019

Optimal coding and the origins of Zipfian laws

The problem of compression in standard information theory consists of as...
02/07/2019

Rank-metric codes

This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theo...