Further factorization of xn − 1 over a finite field (II)-Reference-Cited by-同舟云学术

Further factorization of xn − 1 over a finite field (II)

Published:2021-02-01 Issue:06 Volume:13 Page:
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Wu Yansheng¹,Yue Qin²³

Affiliation:

1. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China

2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

3. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing 100878, P. R. China

Abstract

Let [Formula: see text] be a finite field with [Formula: see text] elements. Let [Formula: see text] be a positive integer with radical [Formula: see text], namely, the product of distinct prime divisors of [Formula: see text]. If the order of [Formula: see text] modulo [Formula: see text] is either 1 or a prime, then the irreducible factorization and a counting formula of irreducible factors of [Formula: see text] over [Formula: see text] were obtained by Martínez, Vergara and Oliveira, Explicit factorization of [Formula: see text], Des. Codes Cryptogr. 77(1) (2015) 277–286 and Wu, Yue and Fan, Further factorization of [Formula: see text] over a finite field, Finite Fields Appl. 54 (2018) 197–215. In this paper, we explicitly factorize [Formula: see text] into irreducible factors in [Formula: see text] and calculate the number of the irreducible factors when the order of [Formula: see text] modulo [Formula: see text] is a product of two primes.

Funder

NUPTSF

National Natural Science Foundation of China

Foundation of Science and Technology on Information Assurance Laboratory

Publisher

World Scientific Pub Co Pte Ltd

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830921500701

Reference18 articles.

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2. Explicit factorization ofX2mpn−1over a finite field

3. A class of minimal cyclic codes over finite fields

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