THE METHOD OF GENERATION OF NONLINEAR PSEUDOCASUAL SEQUENCE WITHOUT USE OF FEEDBACKS
DOI:
https://doi.org/10.26906/SUNZ.2018.4.144Keywords:
рseudocasual sequence, shift registerAbstract
The subject of the research in this article is the process of obtaining a pseudocasual sequence based on the use of the coupling matrix in the finite field GF (3). The goal is to develop a method for obtaining a pseudocasual sequence in a finite field GF (3), based on the use of the coupling matrix as the main generation element. The task: based on the analysis of known approaches to sequence generation, develop a method that, in comparison with a binary shift register, allows increasing the length of the sequence. The approaches used are: obtaining a mathematical pattern for generating a new state on the basis of the previously obtained one and obtaining a generator circuit that implements these regularities. The following results are obtained: the method for obtaining a pseudo-random sequence in a finite field GF (3), based on the use of the coupling matrix as the main generation element. A mathematical apparatus describing the functioning of the shift register with nonlinear feedbacks and its functional scheme is given. The paper shows an example of the formation of the first state of the register. In addition, an example of the regularity of the ring arrangement of columns of coupling matrices is given. As a result, a scheme for generating a sequence without the use of feedbacks is proposed, as in the classical shift register. This allows you to generate sequences for any chosen polynomial that satisfies the condition of obtaining the maximum generation period. Conclusions. The method presented in the form of the obtained expression is proposed, it makes it possible to determine all the columns of the state matrix H without performing calculations and to be applicable to the determination of the SRS using a primitive non-reduced characteristic polynomial. In the proposed method, there are no feedbacks, as in the classical shift register, and therefore, a PRSP can be generated for any chosen polynomial that satisfies the condition for obtaining the maximum generation period.Downloads
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