Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

Abstract

We define a family of quaternary sequences over the residue class ring modulo $4$ of length $pq$, a product of two distinct odd primes, using the generalized cyclotomic classes modulo $pq$ and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences.