Further factorization of $x^n-1$ over a finite field

Autor:	Wu, Yansheng, Yue, Qin, Fan, Shuqin
Rok vydání:	2017
Předmět:	Computer Science - Information Theory Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Let $\Bbb F_q$ be a finite field with $q$ elements and $n$ a positive integer. Mart\'inez, Vergara and Oliveira \cite{MVO} explicitly factorized $x^{n} - 1$ over $\Bbb F_q$ under the condition of $rad(n)|(q-1)$. In this paper, suppose that $rad(n)\nmid (q-1)$ and $rad(n)|(q^w-1)$, where $w$ is a prime, we explicitly factorize $x^{n}-1$ into irreducible factors in $\Bbb F_q[x]$ and count the number of its irreducible factors.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.07943 Zobrazit plný text záznamu View this record from Arxiv