Trace Representation and Linear Complexity of Binary Sequences Derived from Euler Quotients Modulo pqm

In this paper, a generic construction of binary sequences with period [Formula: see text] is presented based on the Euler quotient modulo [Formula: see text], where [Formula: see text] and [Formula: see text] are odd primes satisfying [Formula: see text], and [Formula: see text] is an arbitrary positive integer. Under the assumption that [Formula: see text], the trace representation and linear complexity of the constructed sequences are determined by computing their discrete Fourier transforms. We also determine the least positive period for these sequences. Moreover, an efficient algorithm for computing the linear complexity and the least positive period is presented.