Work

The Eigenvalue Method in coding theory

Year: 2025

Type: article

Abstract: We lay down the foundations of the Eigenvalue Method in coding theory. The method uses modern algebraic graph theory to derive upper bounds on the size of error-correcting codes for various metrics, addressing major open questions in the field. We identify the core assumptions that allow applying the Eigenvalue Method, test it for multiple well-known classes of error-correcting codes, and compare the results with the best bounds currently available. By applying the Eigenvalue Method, we obtain new bounds on the size of error-correcting codes that often improve the state of the art. Our results show that spectral graph theory techniques capture structural properties of error-correcting codes that are missed by classical coding theory approaches.

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x25101600

Authors: Aida Abiad, Loes Peters, Alberto Ravagnani

Institutions: Vrije Universiteit Brussel, Eindhoven University of Technology

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: University of Cambridge, Nederlandse Organisatie voor Wetenschappelijk Onderzoek