Near-Optimal Zero Correlation Zone Sequence Sets from Paraunitary Matrices

Zero correlation zone (ZCZ) sequence sets play an important role in interference-free quasi-synchronous code-division multiple access communications. In this paper, for the first time, we investigate the periodic correlation properties of polyphase sequences obtained from paraunitary (PU) matrices, which shows the inherent relationship between PU matrix and ZCZ sequence sets. Our investigation suggests that any arbitrary PU matrix can produce ZCZ sequence sets by controlling its expanded form. The key idea is to impose certain restrictions on the expanded forms of the PU matrices to enable precise computation of the periodic correlation functions of the constructed sequences. We show that our proposed construction leads to near-optimal ZCZ sequence sets with regard to the ZCZ set size upper bound

On the Noncyclic Property of Sylvester Hadamard Matrices

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On The Relative Abundance of Nonbinary Sequences with Perfect Autocorrelations

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however very rare. We recall a technique that yields examples of nonbinary sequences with perfect autocorrelation over enlarged PSK (PSK+) alphabets. It turns out that there are a large number of existing sequence constructions that we can utilize yield perfect correlation sequences, and that this affords a large number of choices for the length and alphabet of such sequences. We have also considered sequences with ideal autocorrelation with respect to their LPI/LPD properties and obtained initial results in this direction

Low Probability of Intercept properties of some binary sequence families with good correlation properties

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. With the increasingly crowded electromagnetic spectrum, interference between different systems is becoming more important. In this paper, we consider the Low Probability of Intercept properties of some commonly used sequence families, with respect to their triple correlation function. The binary families we consider include the Gold sequence family, the Gold-like sequence family with quadratic span, and the Bent Function sequence family

Nonbinary sequences with perfect and nearly perfect autocorrelations

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however exceedingly rare. We discuss a technique that yields examples of such designs over enlarged PSK (PSK+) alphabets. We also design nearly perfect autocorrelation sequences over enlarged QAM (QAM+) alphabets, compatible with contemporary wireless transmission standards

Efficient identity-based signatures in the standard model

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On partial correlations of various Z4 sequence families

Galois ring m -sequences were introduced in the late 1980s and early 1990s, and have near-optimal full periodic correlations. They are related to Z 4-linear codes, and are used in CDMA communications. We consider periodic correlation and obtain algebraic expressions of the first two partial period correlation moments of the sequences belonging to families A, B and C. These correlation moments have applications in synchronisation performance of CDMA systems using Galois ring sequences. The use of Association Schemes provides us with a new uniform technique for analyzing the sequence families A, B and C

Partial correlations of sequences and their applications

We present an overview of results concerning partial periodic correlation of pseudorandom sequences, ranging from classical results on binary m - sequences to recent results on the first two partial perios correlation moments of the sequences belonging to families A, B and C defined over Galois Rings. The use of Association Schemes provides us with a new uniform technique for analyzing the sequence families A, B and C

A class of quaternary noncyclic Hadamard matrices

A normalized Hadamard matrix is said to be completely noncyclic if no two row vectors are shift equivalent in its punctured matrix (i.e., with the first column removed). In this paper we present an infinite recursive construction for completely noncyclic quaternary Hadamard matrices. These Hadamard matrices are useful in constructing low correlation zone sequences

Secure communication in Mobile Ad Hoc network using efficient certificateless encryption

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