Aidan W. Murphy
Professor Murphy's research interest is in the theory of error-correcting codes, with particular focus on algebraic geometry codes and locally recoverable codes.
Many well-known information storage applications such as QR codes and CD / DVD technologies are based on Reed-Solomon codes, which are able to correct high volumes of errors. However, in the field of distributed storage, the most common scenario is for only one piece of information to be corrupted; in this application, Reed-Solomon codes access much more data than is necessary for error correction, making them relatively inefficient. Locally recoverable codes are designed for this scenario; the aim of locally recoverable codes is to correct single errors by accessing as little information as possible. Algebraic curves, such as Hermitian curves, offer natural structure which is used to correct single errors by accessing less-than-classical amounts of information; the Hermitian-lifted codes of López, Malmskog, Matthews, Piñero-González, and Wootters achieve this goal while simultaneously offering other desirable code parameters.
Professor Murphy's current work focuses in part on the extension of these results to the more general norm-trace curves, and other families of curves traditionally used in algebraic coding theory.
Additionally, he is interested in the methods of fractional decoding applied to these curve-lifted codes, which utilizes properties of the field trace to also correct errors by downloading less information than is normally required.