Name
Abstract | ||
|---|---|---|
Let q be a prime power and let $${\\mathbb {F}}_q$$Fq be a finite field with q elements. This paper discusses the explicit factorizations of cyclotomic polynomials over $$\\mathbb {F}_q$$Fq. Previously, it has been shown that to obtain the factorizations of the $$2^{n}r$$2nrth 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 $$q\\equiv 1 \\pmod p$$qź1(modp), the result can be generalized to the $$p^{n}r$$pnrth 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 $$3^{n}$$3nth, $$3^{n}5$$3n5th and $$3^{n}7$$3n7th cyclotomic polynomials. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10623-016-0224-5 | Des. Codes Cryptography |
Keywords | Field | DocType |
Cyclotomic polynomials,Irreducible factorization,Irreducible polynomials,Finite fields,11T06,11B37,94A60,12Y05 | Discrete mathematics,Wilson polynomials,Combinatorics,Orthogonal polynomials,Classical orthogonal polynomials,Cyclotomic polynomial,Macdonald polynomials,Gegenbauer polynomials,Discrete orthogonal polynomials,Difference polynomials,Mathematics | Journal |
Volume | Issue | ISSN |
83 | 1 | 0925-1022 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hongfeng Wu | 1 | 6 | 5.53 |
| Li Zhu | 2 | 0 | 0.68 |
| Rongquan Feng | 3 | 117 | 25.64 |
| Siman Yang | 4 | 1 | 2.38 |