Description and applications of binomial numeral systems
Олексій Андрійович Борисенко, Алексей Андреевич Борисенко, Oleksii Andriiovych Borysenko, Viacheslav V. Kalashnikov, Вячеслав Витальевич Калашников, Viacheslav Vitaliiovych Kalashnikov, Наталія Іванівна Калашнікова, Наталія Іванівна Калашнікова, Наталія Іванівна Калашнікова, Denys Gutenko · Electronic Sumy State University Institutional Repository (Sumy State University) · 2014
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.