Binomial Numeral Systems: Description and Applications to Numeration Problems
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, J. Watada, Denys Gutenko · 2011
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 ap- plications in the information transmission, processing, and storage due to their error-detection capabili- ties. 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 pre- sented, 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. Keywords Generalized positional numeral systems, Binomial numeral systems, Constant weight codes.