Degree
Doctor of Philosophy
Program
Computer Science
Supervisor
Eric Schost
2nd Supervisor
Jan Minac
Joint Supervisor
Abstract
We present algorithms to construct and perform computations in algebraic closures of finite fields. Inspired by algorithms for constructing irreducible polynomials, our approach for constructing closures consists of two phases; First, extension towers of prime power degree are built, and then they are glued together using composita techniques. To be able to move elements around in the closure we give efficient algorithms for computing isomorphisms and embeddings. In most cases, our algorithms which are based on polynomial arithmetic, rather than linear algebra, have quasi-linear complexity.
Recommended Citation
Doliskani, Javad, "Computing in Algebraic Closures of Finite Fields" (2015). Electronic Thesis and Dissertation Repository. 3282.
https://ir.lib.uwo.ca/etd/3282