As always, the Institute of Telecommunications surprises with new and impressive articles! With the contribution from the Head of the Institute of Telecommunications research paper “Binomial Number System” is published in MDPI applied science journal.
What the paper is about?
This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number systems (PNS) with conditions and number functions for converting BNS with a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, and multivalued number systems. Generated by BNS, binomial numbers possess the error detection property. A characteristic property of binomial numbers is the ability, on their basis, to form various combinatorial configurations based on the binomial coefficients, e.g., compositions or constant-weight (CW) codes. The theory of positional binary BNS construction and generation of binary binomial numbers are proposed. The basic properties and possible areas of application of BNS researched, particularly for the formation and numbering of combinatorial objects, are indicated. The CW binomial code is designed based on binary binomial numbers with variable code lengths. BNS is efficiently used to develop error detection digital devices and has the property of compressing information.
Scientific novelty
Based on the BNS, digital devices, such as binomial decoders and counters, are effectively developed, which have the property of detecting errors. The binomial code has the data compressing property and allows the generation of CW binomial codes. Binary binomial codes have a novelty compared to known PNS and known binomial codes of different classes. The scientific novelty of this paper lies in the generalization of scientific results in the field of BNS and the method of obtaining them.
The work is open access on mdpi, click on this DOI link to read the full paper.
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