Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Abstract

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets. This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr. Its linear complexity, minimal polynomial, and autocorrelation are investigated. The results show that these sequences have a large linear complexity when 2 ∈ D 1 , which means they can resist the Berlekamp-Massey attack. Furthermore, the autocorrelation values are close to 0 with a probability of approximately 1 − 1/r. Therefore, when r is a big prime, the new sequence has a good autocorrelation.