Linear complexity of a class of pseudorandom sequences over a general finite field

Abstract

Due to their nice algebraic structures and pseudorandom features, generalized cyclotomic sequences have wide applications in simulation, coding and cryptography. Based on the Ding–Helleseth sequence, Bai et al. proposed a class of balanced generalized sequences of length pq. Moreover, they showed that this class of sequences has high linear complexity over a finite field of order two. In this paper, we study the linear complexity and the minimal polynomial of this class of sequences over a general finite field. Results indicate the sequence considered possesses high linear complexity over a general finite field.