Short rank-metric codes and scattered subspaces

Fuente: arXiv
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Autori principali: Lia, Stefano, Longobardi, Giovanni, Marino, Giuseppe, Trombetti, Rocco
Natura: Preprint
Pubblicazione: 2023
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author Lia, Stefano
Longobardi, Giovanni
Marino, Giuseppe
Trombetti, Rocco
author_facet Lia, Stefano
Longobardi, Giovanni
Marino, Giuseppe
Trombetti, Rocco
contents By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.
format Preprint
id arxiv_https___arxiv_org_abs_2306_01315
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Short rank-metric codes and scattered subspaces
Lia, Stefano
Longobardi, Giovanni
Marino, Giuseppe
Trombetti, Rocco
Information Theory
Combinatorics
By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.
title Short rank-metric codes and scattered subspaces
topic Information Theory
Combinatorics
url https://arxiv.org/abs/2306.01315