Work

Eigenvalue bounds and alternating rank-metric codes

Year: 2025

Type: article

Abstract: In this note, we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare our results with Delsarte’s linear programming bound, observing that they give the same value. For small values of the minimum rank distance, we are able to establish the equivalence of the two methods. The problem remains open for larger values.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498825410117

Authors: Aida Abiad, Gianira N. Alfarano, Alberto Ravagnani

Institutions: Eindhoven University of Technology, University College Dublin

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Awards: Invariants of Rank-Metric Codes and Matrix Completions over GF(q) -- A Combinatorial Approach, Structure and Asymptotic Density of Extremal Codes