Results 11 to 20 of about 7,081,606 (216)
On the subfields of cyclotomic function fields [PDF]
Czechoslovak Mathematical Journal, 2013 Let \(K={\mathbb F}_q(T)\) be the rational function field over the finite field with \(q\) elements, where \(q\) ia a power of an odd prime. Let \(P\) be a monic irreducible polynomial in \({\mathcal O}_K={\mathbb F}_q[T]\) of degree \(d>0\), \(K_P=K(\lambda _P)\) be the cyclotomic function field where \(\Lambda _P\) is the set of \(P\)-torsion ...
Zhao, Zhengjun, Wu, Xia
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Remarks on the Coefficients of Inverse Cyclotomic Polynomials
, 2023 Cyclotomic polynomials play an imporant role in discrete mathematics. Recently, inverse cyclotomic polynomials have been defined and investigated.
Andrica, D. +2 more
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On Values of Cyclotomic Polynomials. V [PDF]
, 2003 In this paper, we present three results on cyclotomic polynomials. First, we present results about factorization of cyclotomic polynomials over arbitrary fields K.
Motose, Kaoru, Kaoru Motose
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Unit Reducible Cyclotomic Fields [PDF]
, 2023 In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic fields of conductors $2,3,5,7,8,9,12,15$ are all unit reducible, and show ...
Leibak, Alar +3 more
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Improved Ring LWR-Based Key Encapsulation Mechanism Using Cyclotomic Trinomials
IEEE Access, 2020 In the field of post-quantum cryptography, lattice-based cryptography has received the most noticeable attention. Most lattice-based cryptographic schemes are constructed based on the polynomial ring Rq = Zq[x]/f (x), using a cyclotomic polynomial f (x).
So Hyun Park +3 more
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Fast Implementation of High Power Operation in SM9 [PDF]
Jisuanji gongcheng, 2023 The SM9 algorithm is an identification cipher algorithm based on bilinear pairs. The operation process requires multiple higher power operations of twelve domain expansions, and its computing performance is crucial to the application of the SM9 algorithm
Jiangtao WANG, Rong FAN, Zhe HUANG
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The Discrete Fourier Transform Over the Binary Finite Field
IEEE Access, 2023 The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT.
Sergei Valentinovich Fedorenko
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The Eleventh Power Residue Symbol
Journal of Mathematical Cryptology, 2020 This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11),$ \mathbb{Q}\left( {{\zeta }_{11}} \right), $where 11 is a primitive 11th root of unity.
Joye Marc +3 more
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Cyclotomic Gaudin models with irregular singularities [PDF]
, 2017 Generalizing the construction of the cyclotomic Gaudin algebra from arXiv:1409.6937, we define the universal cyclotomic Gaudin algebra. It is a cyclotomic generalization of the Gaudin models with irregular singularities defined in arXiv:math/0612798.
Young, Charles +3 more
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Construction of Complex Lattice Codes via Cyclotomic Fields
Trends in Computational and Applied Mathematics, 2022 Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized ...
E. D. Carvalho +3 more
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