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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]

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]

Several new classes of binary and p-ary regular bent functions are obtained in this paper. The bentness of all these functions is determined by some exponential sums over finite fields, most of which have close relations with the well-known Kloosterman sums. [ABSTRACT FROM AUTHOR]

In this paper, we revisit a method to produce binary sequences using the most significant bit map from \bf Z4 to the binary field. This method is useful for the construction of binary sequences with low correlation and large family size. There may be more cases where starting with \bf Z4 could help researchers design new low correlation sequences for code-division multiple access application. [ABSTRACT FROM AUTHOR]

Inspired by the previous work of Tu and Deng, we propose two infinite classes of Boolean functions of 2k variables where k\geq 2. The first class contains unbalanced functions having high algebraic degree and nonlinearity. The functions in the second one are balanced and have maximal algebraic degree and high nonlinearity (as shown by a lower bound that we prove; as a byproduct we also prove a better lower bound on the nonlinearity of the Carlet–Feng function). Thanks to a combinatorial fact, first conjectured by the authors and later proved by Cohen and Flori, we are able to show that they both possess optimal algebraic immunity. It is also checked that, at least for numbers of variables n\leq 16, functions in both classes have a good behavior against fast algebraic attacks. Compared with the known Boolean functions resisting algebraic attacks and fast algebraic attacks, both of them possess the highest lower bounds on nonlinearity. These bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables (n\leq 38). Moreover, these values are very good. The infinite class of functions we propose in Construction 2 presents, among all currently known constructions, the best provable tradeoff between all the important cryptographic criteria. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed–Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound. [ABSTRACT FROM AUTHOR]

Three classes of binary sequences of period 4N with optimal autocorrelation value/magnitude have been constructed by Tang and Gong based on interleaving certain kinds of sequences of period N, i.e., the Legendre sequence, twin-prime sequence and generalized GMW sequence. In this paper, by means of sequence polynomials of the underlying sequences, the properties of roots of the corresponding sequence polynomials of the interleaved sequences with period 4N and optimal autocorrelation value/magnitude are discussed in the splitting field of x^N-1. As a consequence, both the minimal polynomials and linear complexities of these three classes of sequences are completely determined except for the case of the sequences obtained from the generalized GMW sequences. For the latter, the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based on m-sequences instead of generalized GMW sequences. [ABSTRACT FROM AUTHOR]

Abstract: A class of permutation polynomials with given form over finite fields is investigated in this paper, which is a further study on a recent work of Zha and Hu. Based on some particular techniques over finite fields, two results obtained by Zha and Hu are improved and new permutation polynomials are also obtained. [Copyright &y& Elsevier]

Let q be an odd prime power and F q 3 be the finite field with q 3 elements. In this paper, we propose two classes of permutation trinomials of F q 3 for an arbitrary odd characteristic based on the multivariate method and some subtle manipulation of solving equations with low degrees over finite fields. Moreover, we demonstrate that these two classes of permutation trinomials are QM inequivalent to all known permutation polynomials over F q 3 . To the best of our knowledge, this paper is the first to study the construction of nonlinearized permutation trinomials of F q 3 with at least one coefficient lying in F q 3 ﹨ F q. [ABSTRACT FROM AUTHOR]