Results 1 to 10 of about 460 (160)
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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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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Improving the efficiency of using multivalued logic tools [PDF]
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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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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Frontiers in Applied Mathematics and StatisticsIt is shown that the problem of the adequacy of psychological testing methods, which are varieties of “projective techniques”, is far from being universally recognized.
Ibragim Suleimenov +5 more
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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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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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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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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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