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The Mathematical Safe Problem and Its Solution (Part 1)
Кібернетика та комп'ютерні технології, 2020 Introduction. The problem of the mathematical safe arises in the theory of computer games and cryptographic applications. The article considers the formulation of the mathematical safe problem and the approach to its solution using systems of linear ...
S. Kryvyi, H. Hoherchak
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Two Families of Optimal Ternary Cyclic Codes With Two Zeros
IEEE Access, 2022 Cyclic codes are an important subclass of linear codes and have wide applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms.
Jinmei Fan, Binseng Wang
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Calculation of Fourier-Galois transforms in reduced binary number systems [PDF]
Компьютерная оптика, 2018 The paper proposes a new method for calculating Fourier-Galois transforms (number-theoretical transforms), which are a modular analog of the discrete Fourier transform.
Vladimir Chernov
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Enumeration of Involutions of Finite Rings
Journal of New Theory, 2021 In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R.
Sajana Shaık, Chalapathi Tekurı
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On Fields with Finite Information Density [PDF]
, 2004 The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory ...
A. Kempf +25 more
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Superregular Matrices over Finite Fields
MathematicsA trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero.
Paulo Almeida +2 more
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Repeated-root constacyclic codes of length $ p_1p_2^t p^s $ and their dual codes
AIMS Mathematics, 2023 Let $ \mathbb{F}_q $ be the finite field with $ q = p^{k} $ elements, and $ p_{1}, p_{2} $ be two distinct prime numbers different from $ p $. In this paper, we first calculate all the $ q $-cyclotomic cosets modulo $ p_1p_2^t $ as a preparation for the ...
Hongfeng Wu, Li Zhu
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A Generalization of APN Functions for Odd Characteristic [PDF]
, 2016 Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on.
Kuroda, Masamichi, Tsujie, Shuhei
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Some Multisecret-Sharing Schemes over Finite Fields
Mathematics, 2020 A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot.
Selda Çalkavur, Patrick Solé
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Counting curves over finite fields
, 2014 This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of cardinality q, but the main emphasis is on results on the Euler ...
van der Geer, Gerard
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