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arXiv · 2509.08917

The Eigenvalue Method in Coding Theory

Aida Abiad·Loes Peters·Alberto Ravagnani
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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.

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BibTeXRIS

Aida Abiad, Loes Peters, Alberto Ravagnani. 2025-09-10. The Eigenvalue Method in Coding Theory. https://doi.org/10.4153/s0008414x25101600

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