Low Correlation Sequences From Linear Combinations of Characters
Low Correlation Sequences From Linear Combinations of Characters
复制标题
来自字符线性组合的低相关序列
DOI：
10.1109/tit.2017.2690318
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发表时间：
2016
影响因子：
2.5
通讯作者：
D. Katz
中科院分区：
文献类型：
--
作者：
K. Boothby;D. Katz
使用有限域的乘法特征的线性组合形成的二值序列对显示，与随机序列对相比，同时实现显着降低的均方自相关值（对中的每个序列）和显着降低的均方相互相关值。如果我们将相互关联的优点因子类比地定义为自相关的优点因子，如果我们将缺点因子定义为优点因子的倒数，则已知随机选择的二值序列对具有平均相互关联的缺点因子为1。我们的构建使序列对的相互相关缺陷因子显著小于1，同时，单个序列的自相关缺陷因子也显著小于1（这也表明性能优于平均水平）。本文研究的序列对提供了自相关和互相关性能的组合，这是使用单个字符组成的序列（如最大线性递归序列（m-序列）和Legendre序列）无法实现的。本文证明了乘性字符线性组合所形成的序列对的自相关和互相关优点因子的精确渐近公式。给出的数据表明，这种渐近行为是由中等长度的序列所近似的。
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared with a random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation values (for each sequence in the pair) and significantly lower mean square crosscorrelation values. If we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation, and if we define demerit factor as the reciprocal of merit factor, then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1. Our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1, and at the same time, the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 (which also indicates better than average performance). The sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters, such as maximal linear recursive sequences (m-sequences) and Legendre sequences. In this paper, exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters. Data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length.
从差分集导出多项式的优点因子
DOI：
10.1016/j.jcta.2016.08.006
发表时间：
2017
期刊：
J. Comb. Theory, Ser. A
影响因子：
--
作者：
Ch. Günther;K.-U. Schmidt
通讯作者：
K.-U. Schmidt