Notes about symmetric m-adic complexity of generalized cyclotomic sequences of order two with period pq

Abstract

In this paper, we consider binary generalized cyclotomic sequences with period pq, where p and q are two distinct odd primes. These sequences derive from generalized cyclotomic classes of order two modulo pq. We investigate the generalized binary cyclotomic sequences as the sequences over the ring of integers modulo m for a positive integer m and study m-adic complexity of sequences. We show that they have high symmetric m-adic complexity. Our results generalize well-known statements about 2-adic complexity of these sequences.