Pattern recognition methods as a base of development of new instruments for investigations in physical chemistry

Сулейменов, И. Э.; Vitulyova, Yelizaveta S.; Shaltykova, Dina; Matrassulova, Dinara K.; Bakirov, Akhat

doi:10.1145/3571697.3573941

2022 the 3rd European Symposium on Software Engineering 2022

DOI: 10.1145/3571697.3573941

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Pattern recognition methods as a base of development of new instruments for investigations in physical chemistry

И. Э. Сулейменов

Yelizaveta S. Vitulyova

Dina Shaltykova

et al.

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2024

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

Bakirov,

Matrassulova,

Vitulyova

et al. 2024

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

Bakirov,

Matrassulova,

Vitulyova

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

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Pattern recognition methods as a base of development of new instruments for investigations in physical chemistry

Cited by 1 publication

References 22 publications

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

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

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