Abstract
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 Boztas and Udaya.
Highlights
Let a = (a0, a1, · · ·, aN−1) and b = (b0, b1, · · ·, bN−1) be two complex sequences of period N
In [17], Zeng, Hu, and Liu presented a novel construction for almost perfect polyphase sequences by interleaving, in which the shift sequence was defined by trace function from the finite field Fq2 to the finite field Fq, and the column sequences form a mutually orthogonal almost perfect sequences pair (MOAPSP for short) of even period ≤ 8 searched by computer
The constructions of [8, 17] with the following characters: (i) The shift sequences were defined by trace functions; (ii) Two sequences used as the column sequences form an MOAPSP. We generalized those results in two ways: (i) Note that trace functions are a special class of difference balanced functions with good difference property, we can present new shift sequences defined by difference balanced functions [16]; (ii) According to be analyzing the examples in [8, 17], column sequences are constructed by using an odd perfect sequence and a perfect sequence of same period
Summary
In [17], Zeng, Hu, and Liu presented a novel construction for almost perfect polyphase sequences by interleaving, in which the shift sequence was defined by trace function from the finite field Fq2 to the finite field Fq, and the column sequences form a mutually orthogonal almost perfect sequences pair (MOAPSP for short) of even period ≤ 8 searched by computer. We generalized those results in two ways: (i) Note that trace functions are a special class of difference balanced functions with good difference property, we can present new shift sequences defined by difference balanced functions [16]; (ii) According to be analyzing the examples in [8, 17], column sequences are constructed by using an odd perfect sequence and a perfect sequence of same period.
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