The linear complexity of quaternary sequences plays an important role in cryptology. In this paper, the minimal polynomial of a class of quaternary sequences with low autocorrelation constructed by generalized cyclotomic sequences pairs is determined, and the linear complexity of the sequences is also obtained.

Pseudo-random sequences with high linear complexity play important roles in many domains. We give linear complexity of generalized cyclotomic quaternary sequences with period pq over Z4 via the weights of its Fourier spectral sequence. The results show that such sequences have high linear complexity.

The 2-adic complexity of binary periodic sequences plays an important role in cryptology. In this paper, by means of the usual Fourier transform, we give a simpler form of the upper bound for 2-adic complexity than related result before. For pn-periodic sequences, we discuss the relation between sequences and their Fourier coefficients. Furthermore, based on the relation, we get the lower bound for the number of pn-periodic sequences with given 2-adic complexity.