Linear Complexity of New Generalized Cyclotomic Sequences of Order Two with Odd Length

Abstract

Based on the generalized cyclotomy of order two with respect to n=p₁^e₁+1p₂^e₂+1…p_t^e_t+1, where p₁, p₂, …,p_t are pairwise distinct odd primes and e₁, e₂,…, e_t are non-negative integers satisfying gcd (p_i^e_i (p_i-1), p_j^e_j (p_j-1)) = 2 for all i ≠ j, this paper constructs a new family of generalized cyclotomic sequences of order two with length n and investigates their linear complexity. In the view of cascade theory, this paper obtains the linear complexity of a representative sequence.