A class of balanced binary sequences with optimal autocorrelation properties
A class of balanced binary sequences with optimal autocorrelation properties
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DOI：
10.1109/tit.1977.1055672
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
A. Lempel;M. Cohn;W. Eastman
中科院分区：
文献类型：
--
作者：
A. Lempel;M. Cohn;W. Eastman
描述了一类具有最优自相关特性的平衡二进制序列的构造。给定任意奇素数\(p\)和任意正整数\(m\)，构造了一个长度为\(p^{m}-1\)的平衡\((\pm1)\)二进制序列，其循环自相关函数\(c(\tau)\)满足\(c(0)=p^{m}-1\)，并且当\(\tau\neq0\)时，若\((p^{m}-1)/2\)为奇数，则\(c(\tau)= +2\)或\(-2\)；若\((p^{m}-1)/2\)为偶数，则\(c(\tau)=0\)或\(-4\)。通过证明每个平衡二进制序列至少有两个不同的异相相关值，且这些值至少与这里得到的值一样大，从而证明了最优性。
The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd prime p and any positive integer m , a balanced ( \pm 1) binary sequence of length p^{m} - 1 whose cyclic autocorrelation function c (\tau) satisfies c (0) = p^{m} - 1 , and, for \tau \neq 0, c (\tau) = +2 or -2 when (p^{m} - 1)/2 is odd, and c(\tau) = 0 or -4 when (p^{m} - 1)/2 is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here.