The principle investigator (PI) proposes to investigate topics concerned with the recent application of algebraic geometry to error-correcting codes--work that showed the existence of a sequence of error-correcting codes that have performance exceeding the previously known Gilbert-Varshamov bound. Specifically the PI will attempt to construct codes using varieties of higher dimension such as surfaces, explicitly describe codes on modular curves, investigate methods of constructing codes having prescribed symmetries using the automorphism group of the underlying curve, and explore efficient decoding algorithms for codes on curves of genus greater than zero.
