An Algorithm for Finding Self-Orthogonal and Self-Dual Codes Over Gaussian and Eisenstein Integer Residue Rings Via Chinese Remainder Theorem [PDF]
IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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The Fourier restriction and Kakeya problems over rings of integers modulo $N$ [PDF]
Discrete Analysis, 2018 The Fourier restriction and Kakeya problems over rings of integers modulo $N$, Discrete Analysis 2018:11, 18 pp. The _Fourier restriction problem_ is the following general question.
Jonathan Hickman, James Wright
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A Review Study on Some Properties of The Structure of Neutrosophic Ring [PDF]
Neutrosophic Sets and Systems, 2023 In this article we use neutrosophy to introduced Particular Structure of neutrosophic ring and studied some theorem and properties according to classical axiomatic ring theory.
Adel Al-Odhari
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Solutions of Some Kandasamy-Smarandache Open Problems About the Algebraic Structure of Neutrosophic Complex Finite Numbers [PDF]
Neutrosophic Sets and Systems, 2023 The aim of this paper is to study the neutrosophic complex finite rings 𝐶(𝑍𝑛 ) 𝑎𝑛𝑑 𝐶(< 𝑍𝑛 ∪ 𝐼 >), and to give a classification theorem of these rings. Also, this work introduces full solutions for 12 Kandasamy-Smarandache open problems concerning these ...
Basheer Abd Al Rida Sadiq
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Montgomery Reduction for Gaussian Integers
Cryptography, 2021 Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers.
Malek Safieh, Jürgen Freudenberger
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On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
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On the size of Diophantine m-tuples in imaginary quadratic number rings
Bulletin of Mathematical Sciences, 2021 A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers.
Nikola Adžaga
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On distribution of the number of semisimple rings of order at most x in an arithmetic progression [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let ℓ and q denote relatively prime positive integers. In this article, we derive the asymptotic formula for the summation Σ_{n≤x, n≡ℓ (mod q)} S(n), where S(n) denotes the number of non-isomorphic finite semisimple rings with n elements.
Thorranin Thansri +2 more
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Gauss Congruences in Algebraic Number Fields
Annales Mathematicae Silesianae, 2022 In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.
Gładki Paweł, Pulikowski Mateusz
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