Results 1 to 10 of about 185 (132)
Khronos, 2016 This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
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Three Authentication Schemes without Secrecy over Finite Fields and Galois Rings
Mathematics, 2021 We provide three new authentication schemes without secrecy. The first two on finite fields and Galois rings, using Gray map for this link. The third construction is based on Galois rings.
Juan Carlos Ku-Cauich +1 more
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On Generalized Galois Cyclic Orbit Flag Codes
Mathematics, 2022 Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes.
Clementa Alonso-González +1 more
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An Efficient Audio Encryption Scheme Based on Finite Fields
IEEE Access, 2021 Finite fields are well-studied algebraic structures with enormous efficient properties which have applications in the fields of cryptology and coding theory.
Dawood Shah +5 more
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Galois groups over rational function fields over skew fields
Comptes Rendus. Mathématique, 2020 Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.
Alon, Gil +2 more
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Optical and THz Galois diffusers [PDF]
Journal of the European Optical Society-Rapid Publications, 2013 Binary surface reliefs with sub-wavelength features making up a pseudorandom pattern based on mathematical Galois fields GF(pm) [1, 2] can scatter incoming waves into a large number of diffraction maxima within a huge solid angle.
Jaax M. +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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Improving the efficiency of using multivalued logic tools
Scientific Reports, 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 ...
Ibragim E. Suleimenov +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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Advanced Engineering Research, 2018 Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used in a number of cryptographic problems.
V. M. Deundyak, N. S. Mogilevskaya
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