TY  - BOOK
AU  - Graner, Anna-Maurin
PY  - 2024
DA  - 2024//
TI  - Irreducible polynomials over finite fields for coding and cryptography
PB  - Universität Rostock
CY  - Rostock
AB  - 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>
UR  - https://purl.uni-rostock.de/rosdok/id00004733
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:28-rosdok_id00004733-8
UR  - https://d-nb.info/1356633250/34
UR  - https://doi.org/10.18453/rosdok_id00004733
DO  - 10.18453/rosdok_id00004733
LA  - English
N1  - vorgelegt von Anna-Maurin Graner
ID  - 1916363288
ER  -