Construction of Irreducible Polynomials Over Finite Fields via Polynomial Composition
Mathematics, Master Thesis, 2012
Prof. Dr. Henning Stichtenoth (Thesis Supervisor), Prof. Dr. Alev Topuzoğlu, Assoc. Prof. Cem Güneri, Assoc. Prof. Berrin Yanıkoğlu, Asst. Prof. Alp Bassa
Date & Time: May 30th 2012 – 11:00
Keywords: Finite fields, irreducible polynomials, polynomial composition methods, linearized polynomials, primitive polynomials, composed product.
The construction of irreducible polynomials over finite fields is currently a strong subject of interest with important applications including coding theory and cryptography. One of the most popular methods of construction of irreducible polynomials is the method of composition of polynomials where irreducible polynomials of relatively higher degrees are generated from irreducible polynomials of relatively lower degrees. In this thesis, we give some polynomial composition methods and several applications of them.