Results 11 to 20 of about 127,631 (176)
Factoring polynomials over large finite fields [PDF]
Mathematics of Computation, 1970 This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GF ( p m ) {\text {GF}}({p^m})
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Exceptional Polynomials over Finite Fields
Finite Fields and Their Applications, 1995 The key breakthrough in the attempts to eliminate candidates for the monodromy groups of an indecomposable exceptional polynomial is generally considered to be the work of Fried et al. in 1993. However, they employed the classification of finite simple groups, among other things. The authors of the paper under review remedy this situation by confirming
Cohen, S.D., Matthews, R.W.
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CONSTRUCTING PERMUTATION POLYNOMIALS OVER FINITE FIELDS [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractIn this paper, we construct several new permutation polynomials over finite fields. First, using the linearised polynomials, we construct the permutation polynomial of the form ${ \mathop{\sum }\nolimits}_{i= 1}^{k} ({L}_{i} (x)+ {\gamma }_{i} ){h}_{i} (B(x))$ over ${\mathbf{F} }_{{q}^{m} } $, where ${L}_{i} (x)$ and $B(x)$ are linearised ...
Qin, Xiaoer, Hong, Shaofang
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Etale and crystalline companions, I [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
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Counting irreducible polynomials over finite fields [PDF]
Czechoslovak Mathematical Journal, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Qichun, Kan, Haibin
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Unimodular polynomial matrices over finite fields [PDF]
Journal of Algebraic Combinatorics, 2020 14 ...
Akansha Arora +2 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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Exceptional planar polynomials [PDF]
, 2014 Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many extensions of
Caullery, Florian +2 more
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Stable polynomials over finite fields
Revista Matemática Iberoamericana, 2014 We use the theory of resultants to study the stability, that is, the property of having all iterates irreducible, of an arbitrary polynomial f over a finite field \mathbb{F}_q
Gómez Pérez, Domingo +3 more
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On permutation polynomials over finite fields
International Journal of Mathematics and Mathematical Sciences, 1987 A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a ...
R. A. Mollin, C. Small
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