Parameters of cumulative codes

DOI №______

Abstract

This article presents the properties and features of digital cumulative codes parameters where the code words are created by adding the elements of natural sequence. It should be noted that along with circular and fractal codes, the cumulative codes are poliparametric ones. The formation of digital cumulative codes is described in the article. The article gives the definition of the main concepts used to enter the parameters of cumulative codes. It is shown that the parameters of cumulative codes can serve as their equivalent and entirely replace them. The demonstrated regulation of cumulative codes is produced at the expense of correlation of code words to another natural number, and as a result, there are cases of pair normalized codes with zero residues (dual multiplicity).The concepts used for description of cumulative codes algorithms are formulated in the article. The described variants of parameters combinations and the types of cumulative codes make it possible to receive various algorithms of fight against the channel errors. According to one parameter (variable) of cumulative code it is possible to identify it and evaluate its fidelity. In terms of additional parameters (advanced options) it is possible to restore the correctness of cumulative code. It has been demonstrated that the use of separate cumulative codes parameters simultaneously increases data exchange fidelity that allows to apply them for protection of confidential information from non-authorized admission. The proposed method gives an opportunity to apply received cumulative codes for both compression of information while its transfer and for protection of information distortion transmitted on communication channels and the control of access to confidential information using various methods of code parameters.

Keywords: natural series; cumulative codes; polyparametric codes; module; the sum of elements of the natural numbers; the double of the normalized codes; the rate; normalized cumulative code word; sequence number of the cumulative code word; the index of the codeword with the binary (dual) magnification; offset; polyparametric cumulative codes; represent the parameters of the cumulative codes; the distorted code combination; code parameters; remainder; dual multiplicity.

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