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首页> 外文期刊>Information Theory, IEEE Transactions on >On the Correlation Distributions of the Optimal Quaternary Sequence Family ${cal U}$ and the Optimal Binary Sequence Family ${cal V}$
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On the Correlation Distributions of the Optimal Quaternary Sequence Family ${cal U}$ and the Optimal Binary Sequence Family ${cal V}$

机译：最佳四元序列族$ {cal U} $和最佳二元序列族$ {cal V} $的相关分布

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摘要

Recently, new optimal Families ${cal S}$ and ${cal U}$ of quaternary sequences have been presented, and the optimal binary sequence Family ${cal V}$ obtained from Family ${cal S}$ under Gray map has been investigated as well. The two sequence Families ${cal U}$ and ${cal V}$ are optimal with respect to the well-known Sidelnikov bound and Welch bound, but their exact correlation distributions are not known until now. In this paper, their exact correlation distributions are completely determined in some cases by making use of exponential sums and the theory of ${bf Z}_4$-valued quadratic forms.
机译：最近，提出了新的最佳族$ {cal S} $和$ {cal U} $的四元序列，并且在Gray映射下从Family $ {cal S} $获得的最优二元序列Family $ {cal V} $具有也进行了调查。两个序列系列$ {cal U} $和$ {cal V} $相对于众所周知的Sidelnikov界和Welch界而言是最佳的，但它们的确切相关分布直到现在才知道。在本文中，它们的确切相关分布在某些情况下是通过使用指数和和$ {bf Z} _4 $值二次型理论来确定的。

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