Pseudorandom sequences with large linear complexity can resist the linear attack. The trace representation plays an important role in analysis and design of pseudorandom sequences. In this letter, we present the construction of a family of new binary sequences derived from Euler quotients modulo pq, where pq is a product of two primes and p divides q-1. Firstly, the linear complexity of the sequences are investigated. It is proved that the sequences have larger linear complexity and can resist the attack of Berlekamp-Massey algorithm. Then, we give the trace representation of the proposed sequences by determining the corresponding defining pair. Moreover, we generalize the result to the Euler quotients modulo pmqn with m≤n. Results indicate that the generalized sequences still have high linear complexity. We also give the trace representation of the generalized sequences by determining the corresponding defining pair. The result will be helpful for the implementation and the pseudorandom properties analysis of the sequences.

In this paper, a new generalized cyclotomy over Zpq is presented based on cyclotomy and Chinese remainder theorem, where p and q are different odd primes. Several new construction methods for binary sequence pairs of period pq with ideal two-level correlation are given by utilizing these generalized cyclotomic classes. All the binary sequence pairs from our constructions have both ideal out-of-phase correlation values -1 and optimum balance property.

In this letter, two new families of quaternary sequences with low four-level or five-level autocorrelation are constructed based on generalized cyclotomy over Z2p. These quaternary sequences are balanced and the maximal absolute value of the out-of-phase autocorrelation is 4.

Binary sequence pairs with optimal periodic correlation have important applications in many fields of communication systems. In this letter, four new families of binary sequence pairs are presented based on the generalized cyclotomy over Z5q, where q ≠ 5 is an odd prime. All these binary sequence pairs have optimal three-level correlation values {-1, 3}.