We study a collection of concepts and theorems that laid the foundation of matchgate computation. This includes the signature theory of planar matchgates, and the parallel theory of characters of not necessarily planar matchgates. Our aim is to present a unified and, whenever possible, simplified account of this challenging theory. ... more >>>

We investigate the autoreducibility and mitoticity of complete sets for several classes with respect to different polynomial-time and logarithmic-space reducibility notions.

Previous work in this area focused on polynomial-time reducibility notions. Here we obtain new mitoticity and autoreducibility results for the classes EXP and NEXP with respect to some restricted ... more >>>

We construct a new list-decodable family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. The function fields underlying these codes are constructed using class field theory, specifically Drinfeld modules of rank $1$, and designed to have an automorphism of large order that is used to ``fold" the AG code. ... more >>>