%0 Book
%T Irreducible polynomials over finite fields for coding and cryptography
%A Graner, Anna-Maurin
%D 2024
%C Rostock
%C Universität Rostock
%G English
%F 1916363288
%O vorgelegt von Anna-Maurin Graner
%O GutachterInnen: Gohar M. Kyureghyan (Universität Rostock) ; Arne Winterhof (Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz)
%O Dissertation Universität Rostock 2024
%X 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>
%L 510
%9 theses
%9 Text
%9 Hochschulschrift
%R 10.18453/rosdok_id00004733
%U https://purl.uni-rostock.de/rosdok/id00004733
%U https://nbn-resolving.org/urn:nbn:de:gbv:28-rosdok_id00004733-8
%U https://d-nb.info/1356633250/34
%U https://doi.org/10.18453/rosdok_id00004733