Description and applications of binomial numeral systems
No Thumbnail Available
Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
ICIC International
Article
Date of Defense
Scientific Director
Speciality
Date of Presentation
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 established.
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
Citation
Description and Applications of Binomial Numeral Systems / A.A. Borisenko, V.V. Kalashnikov, N.I. Kalashnykova, D.V. Gutenko // International Journal of Innovative Computing, Information and Control. - 2014. - Vol. 10, No. 1, P. 57-66.