Results 31 to 40 of about 12,820,749 (293)
A Class of Polynomials over Finite Fields
Finite Fields and Their Applications, 1999 A fundamental and difficult problem in Algebraic Curve Theory over Finite Fields is the computation of the maximal number \(N_q(g)\) of \(\mathbb F_q\)-rational points that a projective, geometrically irreducible, non-singular algebraic curve of genus \(g\) defined over \(\mathbb F_q\) can have. \textit{J.-P.
Garcia, Arnaldo, Stichtenoth, Henning
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Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems
Journal of Mathematical Cryptology, 2015 T. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽2.
Alam Bilal, Özbudak Ferruh, Yayla Oğuz
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Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields
IEEE Access, 2020 Compressed Sensing (CS) is a new signal processing theory under the condition that the signal is sparse or compressible. One of the central problems in compressed sensing is the construction of sensing matrices.
Xuemei Liu, Lihua Jia
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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 the Structure of Valiant's Complexity Classes [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of polynomials over a field. We further develop this theory in the spirit of structural complexity and obtain analogues of well-known results by Baker, Gill, and
Peter Bürgisser
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Characterization and Enumeration of Good Punctured Polynomials over Finite Fields
International Journal of Mathematics and Mathematical Sciences, 2016 A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field F2.
Somphong Jitman +4 more
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Polynomials over Finite Fields
, 2020 U ovom radu bavili smo se polinomima i njihovim svojstvima, a posebno svojstvima polinoma nad konačnim poljima. U prvom poglavlju dane su osnovne definicije i tvrdnje vezane uz djeljivost polinoma, faktorizaciju, korijene i ireducibilnost polinoma ...
Bročić, Lucija
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Constructing irreducible polynomials with prescribed level curves over finite fields
International Journal of Mathematics and Mathematical Sciences, 2001 We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.
Mihai Caragiu
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Factoring polynomials over arbitrary finite fields
, 2000 We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields.
Lange, T. +3 more
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Problems on Permutation and Irreducible Polynomials Over Finite Fields [PDF]
, 2018 This integrated thesis is dedicated to the study of polynomials over finite fields, notably permutation polynomials and their compositional inverses, existence of irreducible polynomials with prescribed coefficients, as well as ennumeration of N-free and
Tuxanidy Torres, Aleksandr
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