Cross-Correlation Distribution between a p-Ary m-Sequence and Its Decimated Sequence with Decimation Factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$
Summary :
Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence ${tr_1^n(alpha^i)}$ and its decimated sequence ${tr_1^n(alpha^{di})}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.5 pp.1103-1112
- Publication Date
- 2014/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.1103
- Type of Manuscript
- PAPER
- Category
- Communication Theory and Signals
Authors
Yongbo XIA
South-Central University for Nationalities
Shaoping CHEN
South-Central University for Nationalities
Keyword
Latest Issue
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Yongbo XIA, Shaoping CHEN, "Cross-Correlation Distribution between a p-Ary m-Sequence and Its Decimated Sequence with Decimation Factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 5, pp. 1103-1112, May 2014, doi: 10.1587/transfun.E97.A.1103.
Abstract: Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence ${tr_1^n(alpha^i)}$ and its decimated sequence ${tr_1^n(alpha^{di})}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1103/_p
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@ARTICLE{e97-a_5_1103,
author={Yongbo XIA, Shaoping CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cross-Correlation Distribution between a p-Ary m-Sequence and Its Decimated Sequence with Decimation Factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$},
year={2014},
volume={E97-A},
number={5},
pages={1103-1112},
abstract={Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence ${tr_1^n(alpha^i)}$ and its decimated sequence ${tr_1^n(alpha^{di})}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.},
keywords={},
doi={10.1587/transfun.E97.A.1103},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - Cross-Correlation Distribution between a p-Ary m-Sequence and Its Decimated Sequence with Decimation Factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1103
EP - 1112
AU - Yongbo XIA
AU - Shaoping CHEN
PY - 2014
DO - 10.1587/transfun.E97.A.1103
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2014
AB - Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d= rac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence ${tr_1^n(alpha^i)}$ and its decimated sequence ${tr_1^n(alpha^{di})}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.
ER -
English
