Analysis of linear complexity of generalized cyclotomic $q$-ary sequences of $p^n$ period

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.