The Hermitian Trace Code - Advances in Error-Correcting Codes

Explore a 53-minute lecture on the Hermitian Trace Code presented by Amnon Ta-Shma from Tel-Aviv University as part of the "Advances in the Theory of Error-Correcting Codes" series at the Simons Institute. Delve into the strengthening of the Stepanov-Bombieri approach, which yields powerful bounds on character sum bias over high genus curves. Examine the application of this technique to the Hermitian function field, demonstrating small bias for the quadratic character with low-degree functions of odd degree. Investigate the novel 'universal derivative-fix' lemma and its role in analyzing multiplicity in function fields, connecting derivatives and differentials. Gain insights into non-trivial results for initial levels of the Hermitian tower and the implications for AG codes over constant size fields.

The Hermitian Trace Code