@Book{1916363288,
author="Graner, Anna-Maurin",
title="Irreducible polynomials over finite fields for coding and cryptography",
year="2024",
address="Rostock",
abstract="We present a closed explicit formula for all generating polynomials of a very popular set of codes - the constacyclic codes over finite fields. This problem is equivalent to the factorization of the polynomial X^n-a into monic irreducible factors over a finite field for all positive integers n. From our explicit formula for this factorization we also derive the factorization of the n-th cyclotomic polynomial and of any composition of the form f(X^n) where f is an irreducible polynomial. Additionally, we present a construction of a large set of irreducible polynomials of the same degree.<eng>",
school="Universit{\"a}t Rostock",
note="vorgelegt von Anna-Maurin Graner",
note="GutachterInnen: Gohar M. Kyureghyan (Universit{\"a}t Rostock) ; Arne Winterhof (Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz)",
note="Dissertation Universit{\"a}t Rostock 2024",
doi="10.18453/rosdok_id00004733",
url="https://purl.uni-rostock.de/rosdok/id00004733",
url="https://nbn-resolving.org/urn:nbn:de:gbv:28-rosdok_id00004733-8",
url="https://d-nb.info/1356633250/34",
url="https://doi.org/10.18453/rosdok_id00004733",
language="English"
}