## IACR paper details

Title | On Asymptotic Behavior of the Ratio Between the Numbers of Binary Primitive and Irreducible Polynomials |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2007 |
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URL | http://eprint.iacr.org/2007/301 |
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Author | Yuri Borissov |
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Author | Moon Ho Lee |
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Author | Svetla Nikova |
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Abstract |
In this paper we study the ratio $\theta(n) = \frac{\lambda_2(n)}{\psi_2(n)}$,
where ${\lambda_2(n)}$ is the number of primitive polynomials and
${\psi_2(n)}$ is the number of irreducible polynomials in
$GF(2)[x]$ of degree $n$. %and $2n$, for an arbitrary odd number $n$.
Let $n=\prod_{i=1}^{\ell} p_i^{r_i}$ be the prime factorization of $n$, where $p_i$ are odd primes.
We show that $\theta(n)$ tends to 1 and $\theta(2n)$ is asymptotically
not less than 2/3 when $r_i$ are fixed and $p_i$ tend to infinity. We also, describe an infinite
series of values $n_{s}$ such that $\theta(n_{s})$ is strictly
less than $\frac{1}{2}$. |
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Search for the paper

@misc{eprint-2007-13581,
title={On Asymptotic Behavior of the Ratio Between the Numbers of Binary Primitive and Irreducible Polynomials},
booktitle={IACR Eprint archive},
keywords={},
url={http://eprint.iacr.org/2007/301},
note={Extended abstract of a talk at Finite Fields and applications (FQ8), Melbourne, Australia, July 2007 svetla.nikova@esat.kuleuven.be 13740 received 2 Aug 2007, last revised 15 Aug 2007},
author={Yuri Borissov and Moon Ho Lee and Svetla Nikova},
year=2007
}

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