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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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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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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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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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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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