Linear Recurring Sequences and Explicit Factors of x2nd-1 in Fq[x]

• 作者: Manjit Singh
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 563-574
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386720000462

摘要

Let Fq be a finite field of odd characteristic containing q elements,and n be a positive integer.An important problem in finite field theory is to factorize xn-1 into the product of irreducible factors over a finite field.Beyond the realm of theoretical needs,the availability of coefficients of irreducible factors over finite fields is also very important for applications.In this paper,we introduce second order linear recurring sequences in Fq and reformulate the explicit factorization of x2nd-1 over Fq in such a way that the coefficients of its irreducible factors can be determined from these sequences when d is an odd divisor of q + 1.