## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

AMC

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 $m=2$.

AMC

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.

AMC

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.

AMC

A construction of

*2*^{2n}-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.
AMC

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.

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