# On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

Borissov, Yuri; Ho Lee, Moon; Nikova, Svetla

Serdica Journal of Computing (2008)

- Volume: 2, Issue: 3, page 239-248
- ISSN: 1312-6555

## Access Full Article

top## Abstract

top## How to cite

topBorissov, Yuri, Ho Lee, Moon, and Nikova, Svetla. "On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials." Serdica Journal of Computing 2.3 (2008): 239-248. <http://eudml.org/doc/11464>.

@article{Borissov2008,

abstract = {This work was presented in part at the 8th International Conference on Finite Fields and
Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.In this paper, we study the ratio θ(n) = λ2 (n) / ψ2 (n), where λ2 (n) is
the number of primitive polynomials and ψ2 (n) is the number of irreducible
polynomials in GF (2)[x] of degree n. Let n = ∏ pi^ri, i=1,..l
be the prime factorization of n. We show that, for fixed l and ri , θ(n) is close to 1 and θ(2n) is
not less than 2/3 for sufficiently large primes pi . We also describe an infinite
series of values ns such that θ(ns ) is strictly less than 1/2.},

author = {Borissov, Yuri, Ho Lee, Moon, Nikova, Svetla},

journal = {Serdica Journal of Computing},

keywords = {Finite Fields; Primitive and Irreducible Polynomials; irreducible polynomials; primitive polynomials; finite fields},

language = {eng},

number = {3},

pages = {239-248},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials},

url = {http://eudml.org/doc/11464},

volume = {2},

year = {2008},

}

TY - JOUR

AU - Borissov, Yuri

AU - Ho Lee, Moon

AU - Nikova, Svetla

TI - On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

JO - Serdica Journal of Computing

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 2

IS - 3

SP - 239

EP - 248

AB - This work was presented in part at the 8th International Conference on Finite Fields and
Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.In this paper, we study the ratio θ(n) = λ2 (n) / ψ2 (n), where λ2 (n) is
the number of primitive polynomials and ψ2 (n) is the number of irreducible
polynomials in GF (2)[x] of degree n. Let n = ∏ pi^ri, i=1,..l
be the prime factorization of n. We show that, for fixed l and ri , θ(n) is close to 1 and θ(2n) is
not less than 2/3 for sufficiently large primes pi . We also describe an infinite
series of values ns such that θ(ns ) is strictly less than 1/2.

LA - eng

KW - Finite Fields; Primitive and Irreducible Polynomials; irreducible polynomials; primitive polynomials; finite fields

UR - http://eudml.org/doc/11464

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.