The Linear Complexity of Whiteman’s Generalized Cyclotomic Sequences of Period

In this paper, we mainly get three results. First, let , be distinct primes with ; we give a method to compute the linear complexity of Whiteman’s generalized cyclotomic sequences of period . Second, if , we compute the exact linear complexity of Whiteman’s generalized cyclotomic sequences. Third, if , , and we fix a common primitive root of both and , then , which is a subgroup of the multiplicative group , if and only if Whiteman’s generalized cyclotomic numbers of order 4 depend on the decomposition with .