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| THE ESTIMATION OF THE CORRELATIONS OFA CLASS OF BINARY SEQUENCES |
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Citation： |
DAI ZONGDUO,NI LUQUN,YANG JUNHUI,CHEN WENDE.THE ESTIMATION OF THE CORRELATIONS OFA CLASS OF BINARY SEQUENCES[J].Chinese Annals of Mathematics B,1980,1(2):207~213 |
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Net amount： 856 |
Authors： |
DAI ZONGDUO; NI LUQUN;YANG JUNHUI;CHEN WENDE |
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| Abstract： |
Suppose a(n，m)is a binary sequence
\[\begin{gathered}
\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a} = ({a_1},{a_2},...,{a_n}),{a_i} = 0{\kern 1pt} {\kern 1pt} {\kern 1pt} or{\kern 1pt} {\kern 1pt} {\kern 1pt} 1; \hfill \ m = \sum\limits_{i = 1}^n {{a_i}} ; \hfill \ \mathcal{T}(\tau ) = \sum\limits_{i = 1}^{n - \tau } {a{}_i} {a_{i + \tau }}; \hfill \ P(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a} ) = \mathop {max}\limits_{1 \leqslant \tau \leqslant n - 1} \mathcal{T}(\tau ) \hfill \\
\end{gathered} \]
We call P(a) the correlation of the sequence a(n, m) . Given positive integers
n and m，七he binary sequence a（n，m) such that its P(a) is the smallest is called the
optimal sequence. It is useful in practice.
In this paper a lower bound of ihe correlation of the binary sequences a(n, m)
for given positive integers n and m is estimated. At the end of this paper, we listed,
as examples, several optimal sequences for n= 68, m= 30。 |
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