Construction of modular number systems with arbitrary finite ranges

• Autorzy: Selyaninov M.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we deal with the methodology of constructing modular number systems (MNS), named also residue number systems, on arbitrary mathematical structures such as finite groups, rings and Galois fields.

Słowa kluczowe

EN

number system; numerical system; abstract algebra; number theory; coding theory

PL

systemy liczbowe; systemy numeryczne; algebra abstrakcyjna; teoria liczb; teoria kodowania

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2009
• Tom: Vol. 14
• Strony: 105--115
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Selyaninov M.

• Institute of Technical and Informatics Education Jan Długosz University in Częstochowa al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland

Bibliografia

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• [2] A.I. Maltsev. Algebraic Systems. Nauka, Moscow 1970. (In Russian).
• [3] M. Atghia, I. McDonald. Introduction to Commutative Algebra. Mir, Moscow 1972. (In Russian).
• [4] I.M. Vinogradov. Elements of Number Theory.Nauka, Moscow 1981. (In Russian).
• [5] T. Kasami, N. Tokura, E. Ivodari, J. Inagati. Coding Theory. Mir, Moscow 1978. (In Russian).
• [6] A.A. Kolyada, V.V. Revinsky, M.Y. Selyaninov et al. Elements of the theory and applications of modular technique of parallel in formation processing. Modern Problems of Optics, Radiation Materials Science, Informatics, Radiophysics and Electronics. Proc. Sci. Research Inst. Appl. Phys. Probl. Belgosuniversitet, Minsk, vol. 2, pp. 1–51, 1996.(In Russian).
• [7] M.Y. Selyaninov. Theoretical bases of modular codification of algebraic systems. Proc. Nat. Acad. Sci. Belarus, No. 1, 114-119, 2002. (In Russian).
• [8] A.F. Chernyavsky, V.V. Danilevich, A.A. Kolyada, M.Y. Selyaninov. High-speed Methods and Systems of Digital Information Processing. Belgosuniversitet, Minsk 1996. (In Russian).
• [9] M.Y. Selyaninov. Application of numerically-analytical modular computing techniques for performance of additive and multiplicative operations over signals in spaces of orthogonal projections. Rep. Nat. Acad. Sci. Belarus,46 , No. 2, 62–66, 2002. (In Russian).
• [10] M. Selyaninov M. Modular technique of parallel information processing. Scientific Issues of Jan Długosz University of Czestochowa, Ser.Mathematics, XIII, 43–52, 2008.