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

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.

3-adic complexity of ternary generalized cyclotomic sequences with period

In this paper, we study the ternary generalized cyclotomic sequences with a period equal to a power of an odd prime. Ding-Helleseth’s generalized cyclotomic classes of order three are used for the definition of these sequences. We derive the symmetric 3-adic complexity of above mention sequences and obtain the estimate of symmetric 3-adic complexity of sequences. It is shown that 3-adic complexity of these sequences is large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers.

A Kind of Quaternary Sequences of Period 2pmqn and Their Linear Complexity

Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over F4 with period 2pmqn is constructed using generalized cyclotomic classes. Results show that the linear complexity of these sequences attains the maximum.

2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four

Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

A new class of quaternary generalized cyclotomic sequences of order 2d and length 2pm with high linear complexity

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order [Formula: see text] and length [Formula: see text], which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.