Results 11 to 20 of about 503 (178)
Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]
PLoS ONE, 2023 An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov +2 more
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Noncyclic BCH and Srivastava codes over the subgroup of the groups of units of Galois rings $${G}{R}({{q}}^{{u}},{m})$$ for advanced error control [PDF]
Scientific ReportsThis paper presents a systematic algebraic construction of noncyclic generalizations of BCH and Srivastava codes over Galois rings $$GR\left({q}^{u},m\right).$$ The proposed codes are defined via parity-check matrices whose entries are carefully chosen ...
Muhammad Sajjad +4 more
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A blockchain-based secure data transmission framework in IoT using adaptive deep network with optimized cryptography mechanism [PDF]
Scientific ReportsThis work presents a secure data transmission process in the Internet of Things (IoT). Initially, the required data are collected and given to the Adaptive and Sparse Attention-based Dense Long Short-Term Memory (ASA-DLSTM) network for intrusion ...
Anguraju Krishnan +5 more
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Infinite Towers of Galois Defect Extensions of Kaplansky Fields
Annales Mathematicae Silesianae, 2018 We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of ...
Blaszczok Anna
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Implementation of Galois Field for Application in Wireless Communication Channels
MATEC Web of Conferences, 2018 This paper discusses the implementation of Galois Field based codes for application in wireless communication channel. It discusses the use of Galois Fields outlining the basic performance of a digital communication system in terms of BER curves.
Sarma Dikshita +3 more
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Efficiency of sequence synthesis methods with the «not more than one coincidence» property
Tekhnologiya i Konstruirovanie v Elektronnoi Apparature, 2016 The author presents an expression for determining the minimum possible length of binary sequences with "not more than one coincidence" property. Obtained low bound length value allows quantitatively estimating efficiency of any known synthesis methods ...
A. I. Nevrev, O. N. Galchenkov
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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On finite arithmetic groups [PDF]
International Journal of Group Theory, 2013 Let $F$ be a finite extension of $Bbb Q$, ${Bbb Q}_p$ or a globalfield of positive characteristic, and let $E/F$ be a Galois extension.We study the realization fields offinite subgroups $G$ of $GL_n(E)$ stable under the naturaloperation of the Galois ...
Dmitry Malinin
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Transactions of the London Mathematical Society, 2019 Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels +2 more
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Designing a Block Cipher in Galois Extension Fields for IoT Security
IoT, 2021 This paper focuses on a block cipher adaptation of the Galois Extension Fields (GEF) combination technique for PRNGs and targets application in the Internet of Things (IoT) space, an area where the combination technique was concluded as a quality stream ...
Kiernan George, Alan J. Michaels
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