Polyphase power–residue sequences
Polyphase power–residue sequences
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DOI：
10.1098/rspa.2002.1065
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发表时间：
2003-04
期刊：
影响因子：
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通讯作者：
D. Green;P. Green
中科院分区：
文献类型：
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作者：
D. Green;P. Green
著名的二进制勒让德序列或二次剩余序列的多相版本在三十多年前由Sidelnikov首次描述和分析，但此后很少受到关注。在这里，它表明，这些q相序列的素数长度L也可以构造从索引序列的长度L，或等价地，从陪集的q次幂剩余和非剩余。这些序列也被证明属于两类，其中每一个具有良好定义的周期自相关函数和价值因子。I类序列存在于素数L <$q + 1 mod 2 q和q偶数，而II类序列对应于形式为L <$1 mod 2 q的素数，并且适用于所有q值。I类序列具有幅值小于或等于5的复异相相关值，而对于II类序列，这些是幅值小于或等于3的纯真实的。还研究了其他一些性质。
Polyphase versions of the well–known binary Legendre or quadratic–residue sequences were first described and analysed by Sidelnikov over thirty years ago, but have since received very little attention. Here, it is shown that these q–phase sequences of prime length L can also be constructed from the index sequence of length L or, equivalently, from the cosets of qth power residues and non–residues. These sequences are also shown to fall into two classes, each of which has well–defined periodic autocorrelation functions and merit factors. Class–I sequences exist for prime L ≡ q + 1 mod 2q and q even, whereas class–II sequences correspond to primes of the form L ≡1 mod 2q and are available for all values of q. Class–I sequences have complex out–of–phase correlation values with magnitudes less than or equal to 5, whereas for class–II sequences these are purely real with magnitude less than or equal to 3. Some other properties are also investigated.