The Eigenvalue Method in Coding Theory
By: Aida Abiad, Loes Peters, Alberto Ravagnani
Potential Business Impact:
Makes computer messages more reliable.
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.
Similar Papers
Algebra in Algorithmic Coding Theory
Information Theory
Fixes mistakes in messages sent over the internet.
Primality Testing via Circulant Matrix Eigenvalue Structure: A Novel Approach Using Cyclotomic Field Theory
Symbolic Computation
Finds prime numbers using special math patterns.
On an analogue of the doubling method in coding theory
Number Theory
Creates new math tools for understanding complex codes.