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Вычисление суммы Гаусса с помощью дискретного преобразования Фурье
Дальневосточный математический журнал. 2014. Т. 14. № 1. С. 90–95.
Ustinov A.
The explicit formula for a Gauss sum is proved using the discrete Fourier transform. The Gauss quadratic reciprocity law is established as a corollary.
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ustinov A., Математические заметки 2003 Т. 73 № 1 С. 106–112
The first part of this paper is concerned with the proof of a discrete analog of the Poisson summation formula. In the second part, we describe an elementary proof of a functional equation for the function θ(t), based on the summation formula derived in the paper. ...
Added: October 11, 2025
Sergei Valentinovich Fedorenko, IEEE Access 2023 Vol. 11 P. 62771–62779
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. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and ...
Added: July 19, 2023
Агаларов А. М., Потапов А. А., Рассадин А. Э. et al., Моделирование и анализ информационных систем 2018 Т. 25 № 1 С. 7–17
In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the ...
Added: December 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
Ustinov A., Математические заметки 2022 Т. 112 № 3 С. 478–480
In the paper we proposes a new short proof of the Landsberg-Schaar identity based on finite Fourier series. ...
Added: October 10, 2022
Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2019 Vol. 7 No. 7 P. 13–26
The article introduces the theoretical foundations of the modern method of storing, transmitting and processing signals: digital processing. It’s a way to use relatively small number of values instead of continuous real signal.
For example, when transmitting information in telephony, speech is concentrated in the bandwidth up to 4 kHz. But we need doubled frequency 8 ...
Added: April 9, 2022
Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2020 Vol. 8 No. 6 P. 51–42
Data transmission using orthogonal functions means combining base carrier signals (scaled by numbers of useful information) into one sent signal. Processing the mixed signal after receiving allows dividing it back into carriers and restoring useful numbers.
What is the most compact set of complex sine waves for this? How will the random components of the spectrum ...
Added: April 9, 2022
Semchankau A., Shabanov D. A., Shkredov I., European Journal of Combinatorics 2022 Vol. 100 Article 103453
The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order n. We investigate the number of subset triples (A,B,C) such that for any x from A, y from B, c from C x+y is not equal to z. We prove the tight estimate for this value. As ...
Added: October 26, 2021
Fedorov S., Логачёв О. А., Ященко В. В., Discrete Mathematics and Applications 2020 Vol. 30 No. 2 P. 93–101
Added: June 16, 2021
Evsyutin O., Kokurina A., Мещеряков Р. В. et al., , in: Advances in Intelligent Systems and ComputingVol. 451: Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’16).: Springer, 2016.
On the example of digital images there are investigated properties of the discrete Fourier transform (DFT) used to embed information into the phase spectrum. The investigation helped to form a new steganografic algorithm that can be used in case of non- compressed images. Peculiarity of the algorithm is changeable size of information put into the ...
Added: September 8, 2019
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
Skoltex, 2018.
Proceedings of Sixteenth International Workshop on Algebraic and Combinatorial Coding Theory at Svetlogorsk, Russia,
September 02-08, 2018. ...
Added: September 25, 2018
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
Kalmynin A. B., Mathematical notes 2016 Vol. 99 No. 3 P. 470–476
Added: July 7, 2016