Journal Articles SIAM Journal on Applied Algebra and Geometry Year : 2025

A geometric invariant of linear rank-metric codes

Abstract

Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscross error correction, and post-quantum cryptography. Recent research has focused on constructing new families of rank-metric codes with distinct algebraic structures, emphasizing the importance of invariants for distinguishing these codes from known families and from random ones. In this paper, we introduce a novel geometric invariant for linear rank-metric codes, inspired by the Schur product used in the Hamming metric. By examining the sequence of dimensions of Schur powers of the extended Hamming code associated with a linear code, we demonstrate its ability to differentiate Gabidulin codes from random ones. From a geometric perspective, this approach investigates the vanishing ideal of the linear set corresponding to the rank-metric code.

Fichier principal
Vignette du fichier
Distinguishers_of_rank_metric_codes (17).pdf (451.03 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Licence

Dates and versions

hal-04897043 , version 1 (20-01-2025)

Licence

Identifiers

Cite

Valentina Astore, Martino Borello, Marco Calderini, Flavio Salizzoni. A geometric invariant of linear rank-metric codes. SIAM Journal on Applied Algebra and Geometry, 2025, 9 (4), pp.741-764. ⟨10.1137/24M1713910⟩. ⟨hal-04897043⟩
1133 View
418 Download

Altmetric

Share

  • More