Open AccessPseudo-random sequences of non-maximum length on shift registers with reducible and primitive polynomials
Author(s) -
V. A. Pesoshin,
V. M. Kuznetsov,
A. Kh. Rakhmatullin,
Darya Shirshova
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2052/1/012031
Subject(s) - mathematics , degree (music) , integer (computer science) , combinatorics , polynomial , sequence (biology) , primitive polynomial , modulo , decimation , shift register , primitive root modulo n , cyclotomic polynomial , inverse , discrete mathematics , finite field , mathematical analysis , physics , geometry , computer science , filter (signal processing) , quantum mechanics , biology , acoustics , electronic circuit , computer vision , genetics , programming language
Inhomogeneous pseudo-random sequences of non-maximal length formed by shift registers with linear feedbacks based on a characteristic polynomial of degree n of the form ϕ( x )=ϕ 1 ( x )ϕ 2 ( x ), where ϕ 1 ( x ) = x m 1 ⊕ 1, and ϕ 2 ( x ) of degree m 2 is primitive ( m 1 = 2 k , k is a positive integer, n = m 1 + m 2 ) are considered. Three schemes that are equivalent in terms of periodic sequence structures were considered. Of the greatest interest are the shift registers connected in an arbitrary way using a modulo-two adder, the feedbacks in which correspond to the multipliers ϕ 1 ( x ) and ϕ 2 ( x ) the polynomials ϕ( x ). In this case, there is a complex process of forming output sequences, which involves both direct and inverse M-sequences. The statement about the singularity of the generated sequences at m 1 = 4 is proved, which is confirmed by their decimation with an index equal to the period of the primitive polynomial.