The Fibonacci Numeral System for Computer Vision

Borysenko, Oleksii Andriiovych; Kalashnikov, Vyacheslav V.; Kalashnykova, Nataliya I.; Matsenko, Svitlana

doi:10.1007/978-3-319-67516-9_11

Cited by 4 publications

(2 citation statements)

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“…Mixed base numeral system include the Fibonacci numeral system, factorial and binomial systems, etc. [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that many applications are based on the binomial numeral system, for example, binomial constantweight codes (also called m-of-n codes). They belong to the class of non-linear binary redundant codes used to improve the noise immunity of asymmetric binary communication channels [3,[6][7][8]. The main property of binomial codes, an equal Hamming weight (the number of nonzero elements) of all codewords, is used to effectively detect asymmetric distortions of transmitted sequences.…”

Section: Introductionmentioning

confidence: 99%

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Full Non-Binary Constant-Weight Codes

et al. 2021

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This paper presents the research results of mixed base number systems using binomial representation of numbers. It also shows the investigated non-linear coding techniques with full constant-weight codes, which are based on the binomial numeration. These codes can be used in a variety of computer applications: in code-based cryptosystems; to detect errors in asymmetric communication channels, etc. We propose a new numeral system. It combines the features of positional and binomial numeration. We suggest a technique of full non-binary constant-weight coding based on a generalized binomialpositional representation. It allows us to generalize the known approach to the non-binary case and practically implement computational algorithms for generating full set of non-binary constant-weight sequences. There are the analytical relations that relate the positional and binomial representations of numbers. The article provides several examples, which clear up the usefulness and the constructiveness of the proposed approach, and simplify the perception and understanding of results. We also consider some aspects of the potential use of the proposed numeral system. In particular, the article discusses asymmetric communication channels (the model of a binary Z-channel and its generalization to the non-binary model), and shows the advantage of constant-weight codes for error detection.

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“…Mixed base numeral system include the Fibonacci numeral system, factorial and binomial systems, etc. [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%