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In this correspondence, we present a new family of nonbinary sequences with three-level nontrivial correlations and large linear complexity. The sequences may be considered as nonlinear analogues of the well-known sequences by Trachtenberg and Helleseth. It is shown that the family is optimal with respect to the Welch bound in terms of root mean square of all nontrivial correlations. We also determine the correlation distribution of the new family. Index Terms--Code-division multiple access (CDMA), periodic correlation, pseudorandom sequences, quadratic forms, sequence design.

Coded caching scheme recently has become quite popular in the wireless network, since the maximum transmission amount ${R}$ reduces effectively during the peak-traffic times. To realize a coded caching scheme, each file must be divided into ${F}$ packets, which usually increases the computation complexity of a coded caching scheme. So we prefer to design a scheme with ${R}$ and ${F}$ as small as possible in practice. However, there exists a tradeoff between ${R}$ and ${F}$. In this paper, we generalize the schemes constructed by Shangguan et al. (IEEE Transactions on Information Theory, 64, 5755–5766, 2018) and Yan et al. (IEEE Transactions on Information Theory 63, 5821–5833, 2017), respectively. These two classes of schemes have a wider range of application due to the more flexible memory size than the original ones. By comparing with the previous known deterministic schemes, our new schemes have advantages on ${R}$ or ${F}$. [ABSTRACT FROM AUTHOR]

Ji et al. (IEEE Transactions on Information Theory, 62(2): 849–869, 2016) first studied coded caching in device-to-device (D2D) networks, and proposed a D2D coded caching scheme, which is referred to as the JCM scheme. In practice, we prefer to design a scheme with its two important targets, i.e., the rate (the maximal total amount of transmission) and packet number ${F}$ , as small as possible. In this paper, we first propose a simple array called D2D placement delivery array (DPDA) to characterize the placement phase and the delivery phase in D2D networks. Consequently, some D2D coded caching schemes can be realized by an appropriate DPDA. Second, a lower bound on the rate of a DPDA is derived. And, we show that the JCM scheme achieves our lower bound. However, it is well known that its packet number ${F}$ increases exponentially with the number of users ${K}$. So, we propose two classes of new schemes by constructing DPDAs. One reduces the packet number exponentially with K compared with the JCM scheme while keeping the rate near to our lower bound. The other further reduces ${F}$ to increasing sub-exponentially with ${K}$. [ABSTRACT FROM AUTHOR]

Binary sequences with low odd correlation have important applications in communication systems to reduce interference. In this paper, using the interleaving technique, we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation. As a result, some new binary sequences with optimal odd auto-correlation magnitude are obtained. Besides, two sets consisting of 2^n+1 binary sequences of period 2(2^n-1) with the maximum odd correlation magnitude 2^((n+1)/ 2)+2 are derived, which are the first two optimal classes of binary sequence sets achieving the Sarwate bound on the odd correlation magnitude in the literature. [ABSTRACT FROM PUBLISHER]

As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention in recent years due to its important applications in coding theory and sequence design. One objective of this paper is to present a construction of ZDB functions based on a kind of generalized cyclotomy. It generates ZDB functions over cyclic group with new parameters which can not be produced by earlier constructions. Another objective of this paper is to employ these ZDB functions to obtain at the same time: 1) optimal constant-composition codes; 2) perfect difference systems of sets; and 3) optimal frequency-hopping sequences, all with new parameters. [ABSTRACT FROM PUBLISHER]

Rotation symmetric bent functions and their generation two-rotation symmetric bent functions are two classes of cryptographically significant Boolean functions. However, few constructions have been presented in the literature, which either have restriction on integer $n$ or have algebraic degree no more than 4. In this paper, for any even integer $n\ge 4$ , three classes of bent functions are presented respectively. Most notably, the proposed $n$ -variable rotation symmetric bent functions and two-rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to $n/2$ . Besides, we obtain bent idempotent functions with the maximal algebraic degree $n/2$ . [ABSTRACT FROM PUBLISHER]

Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any K -sparse signal {\boldsymbol{x}} , if a sensing matrix \boldsymbol{A} satisfies the restricted isometry property (RIP) with restricted isometry constant \delta K+1 < 1/\sqrt{K+1}, then under some constraints on the minimum magnitude of nonzero elements of {\boldsymbol{x}} , OMP exactly recovers the support of \boldsymbolx from its measurements \boldsymboly=\boldsymbolA\boldsymbolx+\boldsymbolv in K iterations, where \boldsymbol{v} is a noise vector that is \ell _2 or \ell \infty bounded. This sufficient condition is sharp in terms of \delta K+1 since for any given positive integer K and any 1/\sqrt{K+1}\leq \delta <1, there always exists a matrix \boldsymbol{A} satisfying the RIP with \delta K+1=\delta for which OMP fails to recover a K-sparse signal \boldsymbolx in $K$ iterations. Also, our constraints on the minimum magnitude of nonzero elements of \boldsymbolx are weaker than existing ones. Moreover, we propose worst case necessary conditions for the exact support recovery of \boldsymbolx, characterized by the minimum magnitude of the nonzero elements of \boldsymbolx. [ABSTRACT FROM PUBLISHER]

In this paper, we reinterpret the $(k+2,k)$ zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties, such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property. [ABSTRACT FROM AUTHOR]

New quadratic bent functions in polynomial form are constructed in this paper. The constructions give new Boolean bent, generalized Boolean bent and \(p\) -ary bent functions. Based on \(\boldsymbol {\mathbb {Z}}_{4}\) -valued quadratic forms, a simple method provides several new constructions of generalized Boolean bent functions. From these generalized Boolean bent functions a method is presented to transform them into Boolean bent and semi-bent functions. Moreover, many new \(p\) -ary bent functions can also be obtained by applying similar methods. [ABSTRACT FROM AUTHOR]

In this paper, a class of functions from Niho exponents with four-valued Walsh transform is obtained for any prime by a uniform method, and the distribution of the Walsh transform values is also completely determined. In particular, this class of functions is proven to be bent for a special case. Although it is shown that the obtained bent functions are equivalent to the Leander–Kholosha's class of bent functions, a direct and much simpler proof for the bentness of this kind of Niho functions is provided. [ABSTRACT FROM AUTHOR]

In this paper, a new generalized cyclotomy with respect to a positive odd integer is introduced, and a construction of frequency hopping sequence sets and two constructions of frequency hopping sequences are proposed as its applications. The frequency hopping sequence sets and frequency hopping sequences obtained in this paper can be optimal with respect to the Peng–Fan bound and Lempel–Greenberger bound, respectively. Further, the length of sequences in the optimal frequency hopping sequence sets can be any odd integer larger than 3. Some of them have new parameters. [ABSTRACT FROM PUBLISHER]