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	Explicit factorizations of cyclotomic polynomials over finite fields
	Wu, Hongfeng ; Zhu, Li ; Feng, Rongquan ; Yang, Siman
	2017
关键词	Cyclotomic polynomials Irreducible factorization Irreducible polynomials Finite fields DICKSON POLYNOMIALS
英文摘要	Let q be a prime power and let be a finite field with q elements. This paper discusses the explicit factorizations of cyclotomic polynomials over . Previously, it has been shown that to obtain the factorizations of the th cyclotomic polynomials, one only need to solve the factorizations of a finite number of cyclotomic polynomials. This paper shows that with an additional condition that , the result can be generalized to the th cyclotomic polynomials, where p is an arbitrary odd prime. Applying this result we discuss the factorization of cyclotomic polynomials over finite fields. As examples we give the explicit factorizations of the th, th and th cyclotomic polynomials.; National Natural Science Foundation of China [11101002, 11271129, 61370187]; Beijing Natural Science Foundation [1132009]; General program of science and technology development project of Beijing Municipal Education Commission [KM201510009013]; Shanghai Natural Science Foundation [12ZR1408400]; Fundamental Research Funds for the Central Universities; SCI(E); ARTICLE; 1; 197-217; 83
语种	英语
出处	SCI
出版者	DESIGNS CODES AND CRYPTOGRAPHY
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/474387]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wu, Hongfeng,Zhu, Li,Feng, Rongquan,et al. Explicit factorizations of cyclotomic polynomials over finite fields. 2017-01-01.

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