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http://dx.doi.org/10.14317/jami.2012.30.5_6.903

A NEW PROOF ABOUT THE DECIMATIONS WITH NIHO TYPE FIVE-VALUED CROSS-CORRELATION FUNCTIONS  

Kim, Han-Doo (Institute of Basic Science and Department of Computer Aided Science, Inje University)
Cho, Sung-Jin (Department of Applied Mathematics, Pukyong National University)
Publication Information
Journal of applied mathematics & informatics / v.30, no.5_6, 2012 , pp. 903-911 More about this Journal
Abstract
Let $\{u(t)\}$ and $\{u(dt)\}$ be two maximal length sequences of period $2^n-1$. The cross-correlation is defined by $C_d({\tau})=\sum{_{t=0}^{2^n-2}}(-1)^{u(t+{\tau})+v(t)$ for ${\tau}=0,1,{\cdots},2^n-2$. In this paper, we propose a new proof for finding the values and the number of occurrences of each value of $C_d({\tau})$ when $d=2^{k-2}(2^k+3)$, where $n=2k$, $k$ is a positive integer.
Keywords
Finite field; maximal length sequence; cross correlation functions; Niho's sequence;
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