Recursive constructions of irreducible polynomials over finite fields

Abrahamyan, Sergey; Alizadeh, Mahmood; Kyureghyan, Melsik

doi:10.1016/j.ffa.2012.03.003

Cited by 10 publications

(2 citation statements)

References 5 publications

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“…However, this theorem has a weakness: since no good algorithm is known for constructing "many" irreducible polynomials over F p (see [1], [14], [23], [26]) thus Theorem 1 proves only existence but it does not provide an explicit construction. Thus now we will present another construction which will be more explicit, but the price paid for this is that we will be able to control the cross-correlation of order k only if k = 2 or k is odd.…”

Section: Another Constructionmentioning

confidence: 99%

The cross-correlation measure for families of binary sequences

Gyarmati¹,

Mauduit²,

Sárközy³

2014

Applied Algebra and Number Theory

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Large families of binary sequences of the same length are considered and a new measure, the cross-correlation measure of order k is introduced to study the connection between the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated.

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Section: Another Constructionmentioning

confidence: 99%

The cross-correlation measure for families of binary sequences

Gyarmati¹,

Mauduit²,

Sárközy³

2014

Applied Algebra and Number Theory

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“…A general criteria on the irreducibility of compositions f Q is given in [3]. This criteria is, perhaps, the one used in most of the previous articles: see [8,14], where the rational function Q has degree 2 and [1], where Q has degree p, the characteristic of F q .…”

Section: Introductionmentioning

confidence: 99%

Construction of irreducible polynomials through rational transformations

Panario

Reis

Wang

2020

Journal of Pure and Applied Algebra

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Let F q be the finite field with q elements, where q is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over F q of high degree using rational transformations. In particular, given a divisor D > 2 of q + 1 and an irreducible polynomial f ∈ F q [x] of degree n such that n is even or D ≡ 2 (mod 4), we show how to obtain from f a sequence {f i } i≥0 of irreducible polynomials over F q with deg(f i ) = n · D i .

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The Construction and Determination of Irreducible Polynomials Over Finite Fields

Song

2016

Lecture Notes in Computer Science

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Recursive constructions of irreducible polynomials over finite fields

Cited by 10 publications

References 5 publications

The cross-correlation measure for families of binary sequences

The cross-correlation measure for families of binary sequences

Construction of irreducible polynomials through rational transformations

The Construction and Determination of Irreducible Polynomials Over Finite Fields

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