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Title | Binomial Numeral Systems: Description and Aplications to Numeration Problems |
Authors |
Borysenko, Oleksii Andriiovych
Kalashnikova, Nataliia Ivanivna Kalashnikov, Viacheslav Vitaliiovych 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 |
License | |
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. - 2012. - 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. |
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File | Size | Format | Downloads |
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Binomial_Numeral_Systems_Borysenko.pdf | 240.93 kB | Adobe PDF | -51636043 |
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