Mathematical model of forming vector shift indicators

DOI: 10.31673/2412-9070.2019.054449

Abstract

The vector of displacement indicators is the sequence of decimal numbers formed by summing the number of units obtained by performing one of the binary transformations XOR, OR, AND (with or without negation) of the elements of the initial sequence (first line) of the ring code and the rest of its lines. It should be noted that the vector of displacement indicators is a group integral index of the whole ring code, not its separate line. Each line (code sequence) of a ring code is characterized by a delta factor — the distribution of null and single characters between the two extremes separated by the largest number of null characters for a given initial vector. Ring codes having a delta-type of a certain type form a family of ring codes. VCPs have certain useful properties for identifying ring codes. In particular, they allow the identification of the ring code by its length and the number of single characters in the code sequence, as well as determine the structure of most ring codes. However, the offset vectors cannot be identified by: straight and inverse ring codes, ring codes with symmetrical one-to-one structures of the basic configuration of code sequences, and a separate code sequence within the ring code. Certain deficiencies can be overcome by first distorting the ring code. An in-depth analysis of the set of decimal values of a family of ring codes of type 010101 made it possible to construct a mathematical model of the formation of code sequences of given length N at a given number of m single characters. The analysis of the structure of the vectors of the shift indicators of the code sequences of the classical ring code indicates that all the vectors of the shift indicators have a symmetrical structure.

Keywords: ring codes; vector of shift indicators; code; matrix; binary logic.

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