Results 41 to 50 of about 98,739 (338)
Irreducible polynomials over finite fields produced by composition of quadratics [PDF]
Revista matemática iberoamericana, 2017 For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in $C$ is ...
D. R. Heath-Brown, Giacomo Micheli
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Palindromic Polynomials over Finite Fields
, 2022 For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given for systems of linear equations over $\mathbb{F}$ of index $2$.
Price, Geoffrey L., Thompson, Katherine
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Permutation Polynomials over Finite Fields and their application to Cryptography [PDF]
, 2023 The aim of the paper is the study of Permutation Polynomials over finite fields and their application to cryptography. In this paper, I will begin by a brief review of finite fields, define permutation polynomials over finite fields and their properties.
Benseba, Katia
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Tuples of polynomials over finite fields with pairwise coprimality conditions [PDF]
, 2018 Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions.
Randell Heyman +3 more
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A New Secret Sharing Scheme Based on Polynomials over Finite Fields
Mathematics, 2020 In this paper, we examine a secret sharing scheme based on polynomials over finite fields. In the presented scheme, the shares can be used for the reconstruction of the secret using polynomial multiplication. This scheme is both ideal and perfect.
Selda Çalkavur +2 more
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On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan [PDF]
, 2016 summary:We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the $Q$-transform employed previously by ...
Ugolini, Simone
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A note on inverses of cyclotomic mapping permutation polynomials over finite fields [PDF]
Finite Fields Their Appl., 2016 In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields.
Qiang Wang
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Faster Polynomial Multiplication over Finite Fields [PDF]
Journal of the ACM, 2017 Polynomials over finite fields play a central role in algorithms for cryptography, error correcting codes, and computer algebra. The complexity of multiplying such polynomials is still a major open problem. Let p be a prime, and let M p ( n )
David Harvey +2 more
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A Robust Version of Heged\H{u}s's Lemma, with Applications [PDF]
TheoretiCS, 2023 Heged\H{u}s's lemma is the following combinatorial statement regarding polynomials over finite fields. Over a field $\mathbb{F}$ of characteristic $p > 0$ and for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in \mathbb{F}[x_1 ...
Srikanth Srinivasan
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On coefficients of polynomials over finite fields
Finite Fields and Their Applications, 2011 Let \(\mathbb F_q\) be a finite field and let \(f(x)\) be a polynomial over \(\mathbb F_q\) of degree \(\leq q-1\). The authors begin by giving a formula for the coefficients of \(f(x)\) in terms of the elements of \(\mathbb F_q\) moved by \(f\). This extends a result of \textit{G. L. Mullen} and \textit{B. G. Vioreanu} [Bull. Inst. Comb. Appl. 57, 99--
Amela Muratovic-Ribic, Qiang Wang 0012
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