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Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a combinatorial approach. A generic connection between strictly optimal FHSs and disjoint cyclic perfect Mendelsohn difference families is established. By virtue of this connection, new strictly optimal FHSs are generated from some disjoint CPMDFs. These strictly optimal FHSs have new parameters not covered in the literature. [ABSTRACT FROM AUTHOR]

Let $$p$$ and $$q$$ be two odd primes with $$p=Mf+1$$ and $$M$$ is even. A new construction of $$M$$ -ary sequences of period $$pq$$ with low periodic autocorrelation is presented in this paper based on interleaving the $$M$$ -ary power residue sequence of period $$p$$ according to the quadratic residue with respect to $$q$$ . This construction can generate the well-known twin-prime sequence and generalized cyclotomy sequence of order two if $$M=2$$ . For $$M=4$$ , a new class of quaternary sequences of period $$pq$$ with maximal nontrivial autocorrelation value being either $$\sqrt{5}$$ or $$3$$ is obtained. This achieves the best known results for such kind of quaternary sequences. [ABSTRACT FROM AUTHOR]

Boolean functions with high nonlinearity and good autocorrelation properties play an important role in the design of block ciphers and stream ciphers. In this paper, we give a method to construct balanced Boolean functions of n variables, where n ≥ 10 is an even integer, satisfying strict avalanche criterion (SAC), and with high algebraic degree. Compared with the known balanced Boolean functions with SAC property, the constructed functions possess the highest nonlinearity and the best global avalanche characteristics property. [ABSTRACT FROM AUTHOR]

In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng–Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time. [ABSTRACT FROM PUBLISHER]

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]

Sequences with optimal autocorrelation property are needed in certain communication systems and cryptography. In this paper, a construction of balanced quaternary sequences with period N \equiv 2 (mod\ 4) and optimal autocorrelation value and a construction of almost balanced binary sequences with period N \equiv 0 (mod\ 4) and optimal autocorrelation value are presented. Both constructions are a generalization of earlier ones. [ABSTRACT FROM AUTHOR]

Difference systems of sets (DSS) are important for the construction of codes for synchronization. In this paper, a general construction of optimal and perfect difference systems of sets based on q-ary sequences of period n = −1 (mod q) with difference- balanced property is presented, where q is a prime power. This works for all the known q-ary sequences with ideal autocorrelation, and generalizes the earlier construction based on ternary sequences with ideal autocorrelation. In addition, we construct another class of optimal and perfect difference systems of sets, employing decimation of q-ary d-form sequences of period q m−1 with difference-balanced property, which generalizes the previous construction from power functions. [ABSTRACT FROM AUTHOR]