Binomial Numeral Systems: Description and Aplications to Numeration Problems

Borysenko, Oleksii Andriiovych; Kalashnikov, Viacheslav Vitaliiovych; Kalashnikova, Nataliia Ivanivna; Watada, J.; Gutenko, D.V.

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Title	Binomial Numeral Systems: Description and Aplications to Numeration Problems
Authors	Borysenko, Oleksii Andriiovych Kalashnikov, Viacheslav Vitaliiovych Kalashnikova, Nataliia Ivanivna Watada, J. Gutenko, D.V.
ORCID	http://orcid.org/0000-0001-7466-9135
Keywords	генеровані позиційні системи числення генерируемые позиционные системы счисления generatifed positional numeral systems біноміальні системи числення биномиальные системы счисления binomial numeral systems рівномірні коди равномерные коды constant weight codes
Type	Article
Date of Issue	2011
URI	http://essuir.sumdu.edu.ua/handle/123456789/62088
Publisher	Biomedical Fuzzy Systems Association
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Citation	Binomial Numeral Systems: Description and Aplications to Numeration Problems / A. Borisenko, N.I. Kalashnykova, V.V. Kalashnikov [et al.] // Biomedical Soft Computing and Human Sciences. - 2011. - Vol. 17, No. 2, P. 11–17.
Abstract	We develop a new class of positional numeral systems, namely the binomial ones, which form a subclass of generalized positional numeral systems (GPNS). The binomial systems have wide range of applications in the information transmission, processing, and storage due to their error-detection capabilities. In this paper, the binomial numeral systems are well-defined, their prefix and compactness properties are established. Algorithms of generating binomial coding words (non-uniform and uniform) are presented, as well as an enhanced procedure of construction of constant weight Boolean combinations based upon the non-uniform binomial coding words. The correctness of this procedure is also established.
Appears in Collections:	Наукові видання (ЕлІТ)