Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and 2-adic complexity, have been widely applied to designing reliable stream ciphers. In this paper, we explicitly determine the 2-adic complexities of two classes of generalized cyclotomic binary sequences with order 4. Our results show that the 2-adic complexities of both of the sequences attain the maximum. Thus, they are large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers. We also present some examples to illustrate the validity of the results by Magma programs.

Two new families of balanced almost binary sequences with a single zero element of period L=2q are presented in this letter, where q=4d+1 is an odd prime number. These sequences have optimal autocorrelation value or optimal autocorrelation magnitude. Our constructions are based on cyclotomy and Chinese Remainder Theorem.

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.

In this letter, we present a class of binary sequences with optimal autocorrelation magnitude. Compared with Krengel-Ivanov sequences, some proposed sequences have different autocorrelation distribution. This indicates those sequences would be new. As an application of constructed binary sequences, we derive a class of quaternary sequences of length 4p with autocorrelation magnitude equal to $2sqrt{2}$, which is lower than the autocorrelation magnitude equal to 4 of Chung-Han-Yang sequences given in 2011.

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.

This letter presents a framework, including two constructions, for yielding several types of sequences with optimal autocorrelation properties. Only by simply choosing proper coefficients in constructions and optimal known sequences, two constructions transform the chosen sequences into optimally required ones with two or four times periods as long as the original sequences', respectively. These two constructions result in binary and quaternary sequences with optimal autocorrelation values (OAVs), perfect QPSK+ sequences, and multilevel perfect sequences, depending on choices of the known sequences employed. In addition, Construction 2 is a generalization of Construction B in [5] so that the number of distinct sequences from the former is larger than the one from the latter.

In this paper, we introduce a construction of 16-QAM sequences based on known binary sequences using multiple sequences, interleaved sequences and Gray mappings. Five kinds of binary sequences of period N are put into the construction to get five kinds of new 16-QAM sequences of period 4N. These resultant sequences have 5-level autocorrelation {0, ±8, ±8N}, where ±8N happens only once each. The distributions of the periodic autocorrelation are also given. These will provide more choices for many applications.

An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring ZN , N=pq for two distinct odd primes p and q. The result is a generalization of an estimate of exponential sums on rational point groups of elliptic curves over finite fields. The bound is applied to showing the pseudorandomness of a large family of binary sequences constructed by using elliptic curves over ZN .

Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums. A lower bound on the linear complexity profile is also presented in terms of the correlation measure.

In this letter, new families of binary low correlation zone (LCZ) sequences based on the interleaving technique and quadratic form sequences are constructed, which include the binary LCZ sequence set derived from Gordon-Mills-Welch (GMW) sequences. The constructed sequences have the property that, in a specified zone, the out-of-phase autocorrelation and cross-correlation values are all equal to -1. Due to this property, such sequences are suitable for quasi-synchronous code-division multiple access (QS-CDMA) systems.

In order to eliminate the co-channel and multi-path interference of quasi-synchronous code division multiple access (QS-CDMA) systems, spreading sequences with low or zero correlation zone (LCZ or ZCZ) can be used. The significance of LCZ/ZCZ to QS-CDMA systems is that, even there are relative delays between the transmitted spreading sequences due to the inaccurate access synchronization and the multipath propagation, the orthogonality (or quasi-orthogonality) between the transmitted signals can still be maintained, as long as the relative delay does not exceed certain limit. In this paper, several lower bounds on the aperiodic autocorrelation and crosscorrelation of binary LCZ/ZCZ sequence set with respect to the family size, sequence length and the aperiodic low or zero correlation zone, are derived. The results show that the new bounds are tighter than previous bounds for the LCZ/ZCZ sequences.

In this paper we study the large deviation property for chaotic binary sequences generated by one-dimensional maps displaying chaos and thresholds functions. We deal with the case when nonlinear maps are the r-adic maps. The large deviation theory for dynamical systems is useful for investigating this problem.

Recently, the small set of nonbinary Kasami sequences was presented and their correlation properties were clarified by Liu and Komo. The family of nonbinary Kasami sequences has the same periodic maximum nontrivial correlation as the family of Kumar-Moreno sequences, but smaller family size. In this paper, first it is shown that each of the nonbinary Kasami sequences is unbalanced. Secondly, a new family of nonbinary sequences obtained from modified Kasami sequences is proposed, and it is shown that the new family has the same maximum nontrivial correlation as the family of nonbinary Kasami sequences and consists of the balanced nonbinary sequences.