Results 1 to 10 of about 464 (180)
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 ...
Suleimenov IE +2 more
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Improving the efficiency of using multivalued logic tools. [PDF]
Sci Rep, 2023 Multivalued logics are becoming one of the most important tools of information technology. They are in great demand for creation of artificial intelligence systems that are close to human intelligence, since the functioning of the latter cannot be ...
Suleimenov IE +3 more
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GALOIS FIELD QUANTUM MECHANICS [PDF]
Modern Physics Letters B, 2013 We construct a discrete quantum mechanics (QM) using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser–Horne–Shimony–Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete QM cannot be reproduced with any hidden variable theory.
Chang, Lay Nam +3 more
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LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY [PDF]
Journal of the Institute of Mathematics of Jussieu, 2020 AbstractWe solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over $\mathbb{Q}$. More generally, we show that over such a field, every split differential embedding problem can be solved.
Annette Bachmayr +3 more
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QUANTUM THEORY AND GALOIS FIELDS [PDF]
International Journal of Modern Physics B, 2006 We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one.
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Counting Hopf Galois Structures on Non-Abelian Galois Field Extensions
Journal of Algebra, 1999 If \(L/K\) is a \(G\)-Galois extension of fields, then it is quite possible that \(L/K\) is also Hopf Galois for various Hopf algebras \(H\) which are different from the obvious choice \(H=K[G]\). In particular it was observed by Pareigis and the reviewer that such a ``genuinely Hopf'' Galois structure exists as soon as \(G\) is not abelian.
Carnahan, Scott, Childs, Lindsay
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, 2010 In this paper we study the notion of Smarandache-Galois fields and homomorphism and the Smarandache quotient ring. Galois fields are nothing but fields having only a finite number of elements. We also propose some interesting problems.
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Hopf–Galois structures on Galois field extensions of degree pq
Journal of Pure and Applied Algebra, 2004 Let \(L/K\) be a Galois extension of fields with Galois group \(G\) of order \(pq\) where \(p,q\) are primes with \(p\equiv 1 \pmod q\). The author determines all the Hopf Galois structures on \(L/K\). If \(H\) is a \(K\)-Hopf algebra acting on \(L\), then \(L\otimes H\cong KN\) where \(N\) is a group of order \(pq\).
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Improving the efficiency of using multivalued logic tools: application of algebraic rings. [PDF]
Sci Rep, 2023 Suleimenov IE +3 more
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An algorithm for judging and generating multivariate quadratic quasigroups over Galois fields. [PDF]
Springerplus, 2016 Zhang Y, Zhang H.
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