Maximum Flag-Rank Distance Codes
Combinatorics
2023-03-30 v1 Information Theory
math.IT
Abstract
In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding. In this setting we provide a Singleton-like bound which relates the parameters of a flag-rank-metric code. This allows us to introduce the family of maximum flag-rank distance codes, that are flag-rank-metric codes meeting the Singleton-like bound with equality. Finally, we provide several constructions of maximum flag-rank distance codes.
Keywords
Cite
@article{arxiv.2303.16653,
title = {Maximum Flag-Rank Distance Codes},
author = {Gianira N. Alfarano and Alessandro Neri and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2303.16653},
year = {2023}
}