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College of Engineering/Engineering Practice School (공과대학/대학원)
Dept. of Electrical and Computer Engineering (전기·정보공학부)
Theses (Ph.D. / Sc.D._전기·정보공학부)

Cross-Correlation Between Two Decimated p-ary Sequences : 두 p진 데시메이션 수열 간의 상호상관도

- Authors

- Advisor
- 노종선

- Major
- 공과대학 전기·컴퓨터공학부

- Issue Date
- 2017-02

- Publisher
- 서울대학교 대학원

- Keywords
- Cross-correlation ; decimated sequence ; m-sequence ; p-ary sequence ; sequence

- Description
- 학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 노종선.

- Abstract
- In this dissertation, the cross-correlation between two differently decimated sequences of a $p$-ary m-sequence is considered. Two main contributions are as follows.

First, for an odd prime $p$, $n=2m$, and a $p$-ary m-sequence of period $p^n -1$, the cross-correlation between two decimated sequences by $2$ and $d$ are investigated. Two cases of $d$, $d=\frac{(p^m +1)^2}{2}$ with $p^m \equiv 1 \pmod4$ and $d=\frac{(p^m +1)^2}{p^e +1}$ with odd $m/e$ are considered. The value distribution of the cross-correlation function for each case is completely deterimined. Also, by using these decimated sequences, two new families of $p$-ary sequences of period $\frac{p^n -1}{2}$ with good correlation property are constructed.

Second, an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a $p$-ary m-sequence is derived. The two decimation factors are $2$ and $2(p^m +1)$, where $p$ is an odd prime, $n=2m$, and $p^m \equiv 1 \pmod4$. In fact, these two sequences corresponds to the sequences used for the construction of $p$-ary Kasami sequences decimated by $2$. The upper bound is given as $\frac{3}{2}p^m + \frac{1}{2}$.

Also, using this result, an upper bound of the cross-correlation magnitude between a $p$-ary m-sequence and its decimated sequence with the decimation factor $d=\frac{(p^m +1)^2}{2}$ is derived.

- Language
- English

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