Swan-like results for binomials and trinomials over finite fields of odd characteristic

Authors:
B. Hanson;D. Panario;D. Thomson
Affiliations:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4;School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6;School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6
Venue:
Designs, Codes and Cryptography
Year:
2011

Citing 10
Cited 0

Integer Factoring

Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Irreducible trinomials over finite fields

Mathematics of Computation
Efficient pth root computations in finite fields of characteristic p

Designs, Codes and Cryptography
A note on the reducibility of binary affine polynomials

Designs, Codes and Cryptography
A Swan-like theorem

Finite Fields and Their Applications
On the distribution of irreducible trinomials over F3

Finite Fields and Their Applications
Parity of the number of irreducible factors for composite polynomials

Finite Fields and Their Applications
The parity of the number of irreducible factors for some pentanomials

Finite Fields and Their Applications
Swan's theorem for binary tetranomials

Finite Fields and Their Applications
Factorization of Trinomials over Galois Fields of Characteristic 2

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Swan (Pac. J. Math. 12:1099---1106, 1962) gives conditions under which the trinomial x n + x k + 1 over $${\mathbb{F}_{2}}$$ is reducible. Vishne (Finite Fields Appl. 3:370---377, 1997) extends this result to trinomials over extensions of $${\mathbb{F}_{2}}$$ . In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the finite field $${\mathbb{F}_{q}}$$ , where q is a power of an odd prime.