Binary sequences with high linear complexity and high 2-adic complexity have important applications in communication and cryptography. In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences which have high linear complexity is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, the result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

In this paper, new classes of binary generalized cyclotomic sequences of period 2pm+1qn+1 are constructed. These sequences are balanced. We calculate the linear complexity of the constructed sequences with a simple method. The results show that the linear complexity of such sequences attains the maximum.

In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

Based on the generalized cyclotomy of order two with respect to n=p1e1+1p2e2+1…ptet+1, where p1, p2, …,pt are pairwise distinct odd primes and e1, e2,…, et are non-negative integers satisfying gcd (piei (pi-1), pjej (pj-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.

Based on a unified representation of generalized cyclotomic classes, every generalized cyclotomic sequence of order d over $Z_{p_{1}^{e_{1}}p_{2}^{e_{2}}cdots p_{r}^{e_{r}}}$ is shown to be a sum of d-residue sequences over $Z_{p_{s}^{e_{s}}}$ for $sin {1,2,cdots,r }$. For d=2, by the multi-rate approach, several generalized cyclotomic sequences are explicitly expressed by Legendre sequences, and their linear complexity properties are analyzed.

Let r be an odd prime, such that r≥5 and r≠p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field Frm. Let G(x) be the generating polynomial of the considered quaternary sequences over Fq[x] with q=rm. By explicitly computing the number of zeros of the generating polynomial G(x) over Frm, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to $ rac{1}{2}(3p-1) $ which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.

The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2pm+1qn+1. Furthermore, we establish the formula of the linear complexity of proposed sequences. The results reveal that such sequences with period 2pm+1qn+1 have a good balance property and high linear complexity.

In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field Fr. Our method is based on the use of a pqth root of unity over the extension field, and the representation of the Jacobi sequences by corresponding indicator functions and quadratic characters of two primes p and q.

In this paper, one new class of quaternary generalized cyclotomic sequences with the period 2pq over F4 is established. The linear complexity of proposed sequences with the period 2pq is determined. The results show that such sequences have high linear complexity.

In this letter, we first introduce a new generalized cyclotomic sequence of order two of length pq, then we calculate its linear complexity and minimal polynomial. Our results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for use in stream cipher cryptosystems.

In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for cryptographic applications.

We determine the autocorrelations of the quaternary sequence over F4 and its modified version introduced by Du et al. [X.N. Du et al., Linear complexity of quaternary sequences generated using generalized cyclotomic classes modulo 2p, IEICE Trans. Fundamentals, vol.E94-A, no.5, pp.1214–1217, 2011]. Furthermore, we reveal a drawback in the paper aforementioned and remark that the proof in the paper by Kim et al. can be simplified.

Let p be an odd prime number. We define a family of quaternary sequences of period 2p using generalized cyclotomic classes over the residue class ring modulo 2p. We compute exact values of the linear complexity, which are larger than half of the period. Such sequences are 'good' enough from the viewpoint of linear complexity.

Some new generalized cyclotomic sequences defined by C. Ding and T. Helleseth are proven to exhibit a number of good randomness properties. In this paper, we determine the defining pairs of these sequences of length pm (p prime, m ≥ 2) with order two, then from which we obtain their trace representation. Thus their linear complexity can be derived using Key's method.

In this paper, we calculate autocorrelation of new generalized cyclotomic sequences of period pn for any n > 0, where p is an odd prime number.

In this letter we first introduce a new generalized cyclotomic sequence of order four with respect to pq, then we calculate the linear complexity and minimal polynomial of this sequence. Our results show that the new binary sequence is quite good from the linear complexity viewpoint.