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## The inverse cyclotomic Discrete Fourier Transform algorithm

Ch. 43. P. 185-188.

Приведено доказательство теоремы об обратном циклотомическом DFT над конечным полем.

Sergei Valentinovich Fedorenko, / Preprint. Series Preprint "Preprint". 2016.

In this preprint, we present an example illustrating the novel method for the discrete Fourier transform (DFT) computation based on the Goertzel-Blahut algorithm introduced in the paper "Improving the Goertzel-Blahut algorithm" (IEEE Signal Processing Letters, vol. 23, no. 6, pp. 824-827, 2016). ...

Added: February 3, 2018

Fedorenko Sergei Valentinovich, IEEE Signal Processing Letters 2019 Vol. 26 No. 9 P. 1320-1324

An effective calculation of the Reed-Solomon code syndrome is proposed. The method is based on the use of the partial normalized cyclic convolutions in the partial inverse cyclotomic discrete Fourier transform. The method is the best of the known algorithms, in terms of multiplicative complexity. ...

Added: September 4, 2019

Sergei Valentinovich Fedorenko, IEEE Signal Processing Letters 2016 Vol. 23 No. 6 P. 824-827

A novel method for computing the discrete Fourier transform (DFT) over a finite field based on the Goertzel-Blahut algorithm is described. The novel method is currently the best one for computing the DFT over even extensions of the characteristic two finite field, in terms of multiplicative complexity. ...

Added: January 26, 2018

Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673-38686

A novel method for finding roots of polynomials over finite fields has been proposed.
This method is based on the cyclotomic discrete Fourier transform algorithm.
The improvement is achieved by using the normalized cyclic convolutions,
which have a small complexity and allow matrix decomposition,
as well as methods of adapting the truncated normalized cyclic convolutions calculation.
For small values of ...

Added: April 15, 2021

Fedorenko Sergei Valentinovich, IEEE Transactions on Signal Processing 2020 Vol. 68 P. 4813-4823

The new method for the discrete Fourier transform computation over a finite field is introduced.
This method is a nontrivial generalization of the Duhamel-Hollmann algorithm with replacement
of the Toeplitz convolution calculation by the normalized cyclic convolution calculation.
Both algorithms have the smallest multiplicative complexity. ...

Added: September 12, 2020

Sergei Valentinovich Fedorenko, IEEE Transactions on Signal Processing 2015 Vol. 63 No. 20 P. 5307-5317

A normalized cyclic convolution is a cyclic convolution when one of its factors is a fixed polynomial. Herein, a novel method for constructing a normalized cyclic convolution over a finite field is introduced. This novel method is the first constructive and best known method for even lengths. This method can be applied for computing discrete ...

Added: February 3, 2018

Fedorenko S., СПб. : ГУАП, 2008

Fast algorithms for decoding of linear block codes. ...

Added: February 3, 2018

Alexander Zlotnik, Ilya Zlotnik, / Cornell University. Series "Working papers by Cornell University". 2016. No. 1609.07758.

We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They are based on the well-known Fourier approaches. The key new points are the fast direct and inverse FFT-based algorithms for expansion in eigenvectors ...

Added: September 29, 2016

Wang B., Wu Y., Liu D. et al., The Journal of Physical Chemistry Letters 2023 Vol. 14 No. 37 P. 8289-8295

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system’s structure is adequate and essential fluctuations are sampled, ...

Added: September 7, 2023

Makhaneva A. Y., Zakharova E., Nesterenko S. et al., Journal of Solid State Chemistry 2023 Vol. 322 Article 123969

Mixed calcium-platinum phosphide CaPt4P6 was synthesized using flux-assisted high-temperature ampoule
technique. According to single-crystal XRD data it crystallizes in the monoclinic space group C2/c with Z ¼ 4 (a ¼
8.1361(3) Å, b ¼ 7.9489(3) Å, c ¼ 11.3803(5) Å, β ¼ 90.860(2)o, R1 ¼ 0.0240, wR2 ¼ 0.0618) and belongs to the
BaPt4As6 structure type, the structure ...

Added: October 23, 2023

Nabebin A. A., Социальная политика и социология 2011 № 1 С. 217-227

Приведена группа алгоритмов решения общих систем линейных уравнений в конечных полях, включающая: вычисление определителя, решение квадратной системы линейных уравнений, вычисление обратной матрицы, приведение матрицы к трапециевидной диагональной форме и вычисление ранга матрицы, вычисление фундаментальной системы решений линейных уравнений и алгоритмы решения однородной и неоднородной систем линейных уравнений. ...

Added: May 29, 2012

Evsyutin O., Kokurina A., Мещеряков Р. В. et al., Multimedia Tools and Applications 2018 Vol. 77 No. 21 P. 28567-28599

Many effective methods of the data embedding into digital images are based on the frequency transformations. However use of similar transformations is connected to the following problem: the built-in message is distorted because of information losses in case of restoration of pixels’ integer values from the frequency domain. It represents a vital issue if the ...

Added: September 3, 2019

Vitalii Yu. Kotov, Ivan S. Lunkov, Petr A. Buikin et al., New Journal of Chemistry 2023 Vol. 47 No. 5 P. 2666-2672

A series of hybrid halobismuthate solid solutions [4-Pi2C2]2[Bi2Br10-xIx] (4-PiC2 = 1,1′-(ethane-1,2-diyl)bis(4-methylpyridin-1-ium)) were obtained and structurally characterized. It was shown that upon Br/I substitution, the bromine atoms in the bridging positions of the anion were, first of all, replaced with iodine. In this case, significant and multidirectional deviation of the crystal lattice parameters of the solid solutions ...

Added: January 13, 2023

T.V. Pavlova, S.L. Kovalenko, K.N. Eltsov, Journal of Physical Chemistry C 2020 Vol. 124 No. 15 P. 8218-8224

The structures formed by propylene adsorption on Ni(111) at room temperature are determined by a combination of scanning tunneling microscopy and density functional theory. As a result of the interaction with the Ni(111) surface, propylene molecules are dehydrogenated and coupled into linear hydrocarbon chains. The length of the chains varies from 8 to 60 Å, ...

Added: December 7, 2020

Vyugin I. V., Макарычев С. В., Arnold Mathematical Journal 2019

In this paper we present a new bound of the number of solutions of a polynomial equation $P(x,y)=0$ over the field $\overline{\mathbb{F}}_p$ that belong to a union of cosets $(x,y)\in\bigcup_{i=1}^hg_i'G\times g_i''G$.
This bound improves a case of the bound of Corvaja and Zannier (see \cite{C-Z}) in the case $h\gg 1$. Using this bound we obtain estimates ...

Added: December 14, 2017

Nabebin A. A., Ученые записки Российского государственного социального университета 2012 № 8 С. 140-147

It is given the group of algorithms providing deciphering of linear feedback shift registers, including the tests for irreducibility and primitiveness of polynomials in a finite field; the test: to be the generator for multiplicative group of a finite field; computing of an inverse element; computing of the sum, product, a natural power of elements; ...

Added: August 28, 2013

Morkhova Y., Orlova E., Kabanov A. et al., Solid State Ionics 2023 Vol. 400 Article 116337

The conductivity in the monoclinic polymorphs of Ln2MoO6 (Ln = Sm, Gd, Dy) oxymolybdates was investigated by theoretical and experimental methods. A theoretical approach consisted of geometrical-topological analysis, bond valence site energy, kinetic Monte-Carlo (KMC) modeling and density functional theory (DFT) calculations. The theoretical results have shown that oxygen ionic conductivity is possible in all ...

Added: August 30, 2023

A.S. Vasenko, Agrawal S., Prezhdo O. et al., Journal of Chemical Physics 2022 Vol. 156 No. 9 Article 094702

Graphitic carbon nitride (GCN) has attracted significant attention due to its excellent performance in photocatalytic applications. Non-metal doping of GCN has been widely used to improve the efficiency of the material as a photocatalyst. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we study the charge carrier dynamics in oxygen and ...

Added: March 17, 2022

Fedorenko Sergei Valentinovich, IEEE Access 2022 Vol. 10 P. 110639-110645

A novel method of spectral decoding for systematic BCH codes has been proposed. This method has a simple description and a small computational complexity. ...

Added: October 26, 2022

Avdoshin S. M., Набебин А. А., М. : ДМК Пресс, 2017

The textbook contains necessary information about universal and classical algebras, systems of axioms for the basic algebraic structures (groupoid, monoid, semi-groups, groups, partial orders, rings, fields). The basic cryptographic algorithms are described. Error-correcting codes - linear, cyclic, BCH are considered. Algorithms for designing of such codes are given. Many examples are shown. It is put ...

Added: August 19, 2016

А.А. Злотник, И.А. Злотник, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2017 Т. 473 № 2 С. 131-137

Представлен новый быстрый прямой алгоритм реализации метода конечных элементов (МКЭ) порядка n>=2 на прямоугольниках для решения различных краевых задач для уравнений типа Пуассона. Он обобщает хорошо известный алгоритм для случая разностных схем или билинейных КЭ (n=1), использующий версии быстрого дискретного преобразования Фурье (БДПФ). Его ядром являются быстрые прямой и обратный алгоритмы разложения по собственным векторам ...

Added: October 25, 2016

Vyugin I. V., Солодкова Е. В., Шкредов И. Д., Математические заметки 2016 Т. 100 № 2 С. 185-195

By means Stepanov's method the bound of cardinality of the intersection of additive shifts of several subgroups of multiplicative group of the finite field was obtained. This bound apply to some question of additive decomposition of subgroups. ...

Added: January 29, 2016

Zhao R., Xu S., Liu D. et al., Applied Catalysis B: Environmental 2023 Vol. 338 Article 123027

NiFe layered double hydroxide (LDH) is a non-noble benchmark catalyst for oxygen evolution reaction (OER). However, the mechanism of enhancing catalytic activities via incorporating foreign elements is still not resolved. Herein, we modulate the electronic structure of NiFe LDH by introducing high-valence Zr4+ to synergistically improve catalytic activity. NiFeZr LDH requires overpotential of only 182 mV at ...

Added: November 20, 2023

Norman G., Saitov I., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2016 Vol. 94 No. 043202 P. 043202-1-043202-8

We provide theoretical analysis of the reflectance of shock-compressed plasmas and warm dense matter for normal incidence of laser radiation as well as for the dependence of s- and p-polarized reflectivity on the incidence angle. The self-consistent approach for the calculation of the optical and electronic properties of warm dense matter and nonideal plasmas developed ...

Added: March 30, 2017