Generalizations of Jacobsthal sums and hypergeometric series over finite fields
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DOI: 10.1007/s11139-020-00364-w
Abstract: For non-negative integers $$l_{1}, l_{2},\ldots , l_{n}$$ , we define character sums $$\varphi _{(l_{1}, l_{2},\ldots , l_{n})}$$ and $$\psi _{(l_{1}, l_{2},\ldots , l_{n})}$$ over a finite field which are generalizations of Jacobsthal and modified Jacobsthal… read more here.
Keywords: generalizations jacobsthal; hypergeometric series; finite field; series ... See more keywords
On Diophantine exponents for Laurent series over a finite field
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DOI: 10.1016/j.jnt.2017.09.008
Abstract: Abstract In this paper, we study the properties of Diophantine exponents w n and w n ⁎ for Laurent series over a finite field. We prove that for an integer n ≥ 1 and a… read more here.
Keywords: exponents laurent; finite field; diophantine exponents; laurent series ... See more keywords
Density of Periodic Points for Lattès maps over Finite Field
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DOI: 10.1016/j.jnt.2021.10.009
Abstract: Let Ld be the Lattès map associated to the multiplication-by-d endomorphism of an elliptic curve E defined over a finite field Fq. We determine the density δ(Ld, q) of periodic points for Ld in P(Fq).… read more here.
Keywords: periodic points; points latt; density periodic; finite field ... See more keywords
Transcendence degree one function fields over a finite field with many automorphisms
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2017.08.008
Abstract: Abstract Let K be the algebraic closure of a finite field F q of odd characteristic p . For a positive integer m prime to p , let F = K ( x , y… read more here.
Keywords: finite field; many automorphisms; transcendence degree; field ... See more keywords
Hardware architectures for computing the cosine transforms over the finite field F28$\mathbb {F}_{2^8}$
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DOI: 10.1049/ell2.70097
Abstract: This article presents hardware architectures for computing four types of the 8‐point cosine transforms over the finite field . The proposed architectures utilize three distinct approaches, described in SystemVerilog, and are synthesized on a field‐programmable… read more here.
Keywords: field; cosine transforms; architectures computing; hardware architectures ... See more keywords
On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry
Sign Up to like & getrecommendations! Published in 2021 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnab201
Abstract: The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via… read more here.
Keywords: restriction; restriction conjecture; finite field; field cone ... See more keywords
A Bilinear Approach to the Finite Field Restriction Problem
Sign Up to like & getrecommendations! Published in 2024 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnaf077
Abstract: Let $P$ denote the $3$-dimensional paraboloid over a finite field of odd characteristic in which $-1$ is not a square. We show that the Fourier extension operator associated with $P$ maps $L^{2}$ to $L^{r}$ for… read more here.
Keywords: bilinear approach; field; field restriction; problem ... See more keywords
Area-Efficient Finite Field Multiplication Using Hybrid SET-MOS Technology
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Circuits and Systems I: Regular Papers"
DOI: 10.1109/tcsi.2022.3186810
Abstract: Single-electron transistors (SETs) exhibit a unique characteristic of Coulomb oscillation which can find many digital applications with area efficiency. More specifically, both MOS and SET devices can be used to implement XOR gates with almost… read more here.
Keywords: set mos; area; finite field; hybrid set ... See more keywords
Cluster Synchronization of Finite-Field Networks.
Sign Up to like & getrecommendations! Published in 2023 at "IEEE transactions on cybernetics"
DOI: 10.1109/tcyb.2023.3273571
Abstract: This technical paper investigates the cluster synchronization of finite-field networks (FFNs) based on the algebraic state space representation. By resorting to the semi-tensor product of matrices, the cluster synchronization of an FFN can be completely… read more here.
Keywords: field networks; synchronization finite; finite field; cluster synchronization ... See more keywords
Synchronization of Finite-Field Networks With Time Delays
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DOI: 10.1109/tnse.2021.3115891
Abstract: In this paper, finite-field networks (FFNs) with time delays are investigated. We analyze the dynamics of FFNs with time delays in view of linear recursion theory. It is shown that delayed FFNs behave in a… read more here.
Keywords: time; field networks; finite field; delayed ffns ... See more keywords
An Efficient and High-Speed Overlap-Free Karatsuba-Based Finite-Field Multiplier for FGPA Implementation
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"
DOI: 10.1109/tvlsi.2021.3058509
Abstract: Cryptography systems have become inseparable parts of almost every communication device. Among cryptography algorithms, public-key cryptography, and in particular elliptic curve cryptography (ECC), has become the most dominant protocol at this time. In ECC systems,… read more here.
Keywords: implementation; field; speed overlap; high speed ... See more keywords