Algorithm for Analyzing Rotating Images Based on the Fourier-Galois Transform

Matrassulova, Dinara K.; Kabdushev, Sherniyaz B.; Bakirov, Akhat; Сулейменов, И. Э.

doi:10.1109/iccrd56364.2023.10080084

2023 15th International Conference on Computer Research and Development (ICCRD) 2023

DOI: 10.1109/iccrd56364.2023.10080084

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Algorithm for Analyzing Rotating Images Based on the Fourier-Galois Transform

Dinara K. Matrassulova

Sherniyaz B. Kabdushev

Akhat Bakirov

et al.

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Cited by 2 publications

References 26 publications

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Improving the efficiency of using multivalued logic tools: application of algebraic rings

Suleimenov,

Vitulyova,

Kabdushev

et al. 2023

Sci Rep

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It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic operations. For multivalued logics, the number of variables in which is equal to a prime number, such a connection is naturally established through explicit algebraic expressions in Galois fields. It is possible to define an algebraic δ-function, which allows you to reduce any truth table to an algebraic expression, for the case when the number of values accepted by a multivalued logic variable is equal to an integer power of a prime number. In this paper, we show that the algebraic δ-function can also be defined for the case when the number of values taken by a multivalued logic variable is p − 1, where p is a prime number. This function also allows to reduce logical operations to algebraic expressions. Specific examples of the constructiveness of the proposed approach are presented, as well as electronic circuits that experimentally prove its adequacy.

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Improving the efficiency of using multivalued logic tools: application of algebraic rings

Suleimenov,

Vitulyova,

Kabdushev

et al. 2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

The specifics of the Galois field GF(257) and its use for digital signal processing

Bakirov,

Matrassulova,

Vitulyova

et al. 2024

Sci Rep

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An algorithm of digital logarithm calculation for the Galois field $$GF(257)$$ G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 levels. It is shown that for this case it is advisable to use the specifics of quasi-Mersenne prime numbers, representable in the form $${p=2}^{n}+1$$ p = 2 n + 1 , which includes the number 257. For fields $$GF({2}^{n}+1)$$ G F ( 2 n + 1 ) , an alternating encoding can be used, in which non-zero elements of the field are displayed through binary characters corresponding to the numbers + 1 and − 1. In such an encoding, multiplying a field element by 2 is reduced to a quasi-cyclic permutation of binary symbols (the permuted symbol changes sign). Proposed approach makes it possible to significantly simplify the design of computing devices for calculation of digital logarithm and multiplication of numbers modulo 257. A concrete scheme of a device for digital logarithm calculation in this field is presented. It is also shown that this circuit can be equipped with a universal adder modulo an arbitrary number, which makes it possible to implement any operations in the field under consideration. It is shown that proposed digital algorithm can also be used to reduce 256-valued logic operations to algebraic form. It is shown that the proposed approach is of significant interest for the development of UAV on-board computers operating as part of a group.

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Algorithm for Analyzing Rotating Images Based on the Fourier-Galois Transform

Cited by 2 publications

References 26 publications

Improving the efficiency of using multivalued logic tools: application of algebraic rings

Improving the efficiency of using multivalued logic tools: application of algebraic rings

The specifics of the Galois field GF(257) and its use for digital signal processing

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