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New $M$ -Ary Sequence Families With Low Correlation From the Array Structure of Sidelnikov Sequences

机译:Sidelnikov序列的数组结构中具有低相关性的新 $ M $ -Ary序列族

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In this paper, we extend the construction by Yu and Gong for families of -ary sequences of period from the array structure of an -ary Sidelnikov sequence of period , where is a prime power and . The construction now applies to the cases of using any period for and . The proposed construction results in a family of -ary seqeunces of period with: 1) the correlation magnitudes, which are upper bounded by and 2) the asymptotic size of as increases. We also characterize some subsets of the above of size but with a tighter upper bound on its correlation magnitude. We discuss reducing both time and memory complexities for the- practical implementation of such constructions in some special cases. We further give some approximate size of the newly constructed families in general and an exact count when is a prime power or a product of two distinct primes. The main results of this paper now give more freedom of tradeoff in the design of -ary sequence family between the family size and the correlation magnitude of the family.
机译:在本文中,我们从周期的一元Sidelnikov序列的数组结构扩展了Yu和Gong对周期的一元序列的族的构造,其中分别是素数和。现在的构造适用于对和使用任何周期的情况。所提出的构造导致周期的-ary序列族:1)相关幅度,其上界为2)渐近大小随着增加。我们还表征了上述大小的一些子集,但其相关幅度的上限更严格。我们讨论了在某些特殊情况下,为此类构造的实际实现降低时间和内存的复杂性。我们进一步给出了新建家庭的大致规模,并给出了当是主幂或两个不同素数的乘积时的精确计数。现在,本文的主要结果为在家庭大小和家庭相关程度之间的-ary序列家庭设计中提供了更大的权衡自由。

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