Total codes

DOI №______

Abstract

This article presents numerical cumulative codes. Every cumulative code word is created by way of addition of natural sequence elements. Furthermore every cumulative code word can be represented in the form of binary number. This code is polyparametric code, where each code word has several parameters. The main parameters of the code are determined after it’s normalizing with any prime number upwards of 5. The structure of the cumulative codes detect channel errors. The parameters of the cumulative codes sequence provide errors correction by selecting such code words that satisfy these parameters. One parameter can be used to estimate the accuracy of the cumulative code word. The parameter itself is determined directly by the user. Additional parameters make it possible to restore the correctness of the code word. The properties are demonstrated which is that beginning with any dual multiplicity, the residuals from dividing the integers of the cumulative codes by a given divisor up and down according to the set of sequence numbers are symmetric and pairwise equal to each other, starting with any dual multiplicity. This method makes it possible to implement various methods of code parameters. Rationing allows you to get a number of varieties of codes, and this valuation can be performed at the receiving end. The polyparametricity of cumulative codes allows them to be identified. These cumulative codes can be used to compress information during its transmission, to realize the protection of information from errors, and also to realize the protection of confidential information from unauthorized access. They can also be used to address new processes.

Keywords: numeric natural series; code parameters; code sequence number; code word; digital cumulative codes; code settings; cumulative code word; the value of the cumulative code word; the remainder of the division of the cumulative code word; binary code combination; binary cumulative codes; a countable set of aggregate codes; polyparametrical; remainder; dual multiplicity; external interference; external interference that distorts the structure of the code word.

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