Syllabus
Modular arithmetics for polynomials. Examples of finite fields.
Multiplicative group of a finite field. Möbius function. Irreducible, cyclotomic and primitive polynomials.
Factorization of polynomials. Basic relationships between block codes and finite fields (generating and control matrices, examples of codes).
Quadratic residues. Perron Theorem. Cyclotomic extensions.
Annotation
The aim of this course is to introduce students to the theory of finite fields. Finite fields are presented both as a useful tool in apllications and and as a model case of an algebraic structure deducible from intuitive operations, but demanding a more abstract approach for effective work.
A required course for Information Security.