Open AccessAnalysis of linear complexity of generalized cyclotomic Q-ary sequences of pn period
Author(s) -
Vladimir Edemskiy
Publication year - 2021
Publication title -
vestnik astrahanskogo gosudarstvennogo tehničeskogo universiteta. seriâ: upravlenie, vyčislitelʹnaâ tehnika i informatika
Language(s) - English
Resource type - Journals
eISSN - 2224-9761
pISSN - 2072-9502
DOI - 10.24143/2072-9502-2021-1-70-79
Subject(s) - modulo , primitive root modulo n , mathematics , period (music) , sign (mathematics) , prime (order theory) , combinatorics , sequence (biology) , binary number , recurrence relation , time complexity , discrete mathematics , arithmetic , mathematical analysis , physics , biology , acoustics , genetics
The article presents the analysis of the linear complexity of periodic q-ary sequences when changing k of their terms per period. Sequences are formed on the basis of new generalized cyclotomy modulo equal to the degree of an odd prime. There has been obtained a recurrence relation and an estimate of the change in the linear complexity of these sequences, where q is a primitive root modulo equal to the period of the sequence. It can be inferred from the results that the linear complexity of these sequences does not sign ificantly decrease when k is less than half the period. The study summarizes the results for the binary case obtained earlier.