AMC
Correlation of binary sequence families derived from the multiplicative characters of finite fields
Zilong Wang Guang Gong
In this paper, new constructions of the binary sequence families of period $q-1$ with large family size and low correlation, derived from multiplicative characters of finite fields for odd prime powers, are proposed. For $m ≥ 2$, the maximum correlation magnitudes of new sequence families $\mathcal{S}_m$ are bounded by $(2m-2)\sqrt{q}+2m+2$, and the family sizes of $\mathcal{S}_m$ are given by $q-1$ for $m=2$, $2(q-1)-1$ for $m=3$, $(q^2-1)q^{\frac{m-4}{2}}$ for $m$ even, $m>2$, and $2(q-1)q^{\frac{m-3}{2}}$ for $m$ odd, $m>3$. It is shown that the known binary Sidel'nikov-based sequence families are equivalent to the new constructions for the case $m=2$.
keywords: Binary sequences multiplicative characters correlation Weil bound.
AMC
Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions
Yang Yang Xiaohu Tang Guang Gong
A pair of two sequences is called the even periodic (odd periodic) complementary sequence pair if the sum of their even periodic (odd periodic) correlation function is a delta function. The well-known Golay aperiodic complementary sequence pair (Golay pair) is a special case of even periodic (odd periodic) complementary sequence pair. In this paper, we presented several classes of even periodic and odd periodic complementary pairs based on the generalized Boolean functions, but which do not form Gloay pairs. The proposed sequences could be used to design signal sets, which have been applied in direct sequence code division multiple (DS-CDMA) cellular communication systems.
keywords: Even periodic complementary sequence pair Golay complementary pair odd periodic complementary sequence pair Golay sequences generalized Boolean function.
AMC
New almost perfect, odd perfect, and perfect sequences from difference balanced functions with $d$-form property
Yang Yang Xiaohu Tang Guang Gong
By using shift sequences defined by difference balanced functions with d-form property, and column sequences defined by a mutually orthogonal almost perfect sequences pair, new almost perfect, odd perfect, and perfect sequences are obtained via interleaving method. Furthermore, the proposed perfect QAM+ sequences positively answer to the problem of the existence of perfect QAM+ sequences proposed by Boztaş and Udaya.
keywords: Almost perfect sequences perfect sequences odd perfect sequences QAM+ sequences difference balanced function d-form.
AMC
On $\omega$-cyclic-conjugated-perfect quaternary GDJ sequences
Yang Yang Guang Gong Xiaohu Tang
A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: $\omega$-cyclic-conjugated autocorrelation. As a result, we present several classes of $\omega$-cyclic-conjugated-perfect quaternary Golay sequences, where $\omega=\pm 1$. We also considered such perfect property for $4^q$-QAM Golay sequences, $q\ge 2$ being an integer.
keywords: quaternary sequences quadrature amplitude modulation (QAM) Golay sequence $\omega$-cyclic-conjugated autocorrelation. $\omega$-cyclic autocorrelation Golay-Davis-Jedweb (GDJ) sequences
AMC
A generalized construction of OFDM $M$-QAM sequences with low peak-to-average power ratio
Zilong Wang Guang Gong Rongquan Feng
A construction of 22n-QAM sequences is given and an upper bound of the peak-to-mean envelope power ratio (PMEPR) is determined. Some former work can be viewed as special cases of this construction.
keywords: orthogonal frequency-division multiplexing (OFDM) multicarrier communications peak-to-mean envelope power ratio (PMEPR). Golay sequences QAM

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