On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2
Summary :
Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg { rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $ rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.
- Publication
- IEICE TRANSACTIONS on Communications Vol.E98-B No.3 pp.415-421
- Publication Date
- 2015/03/01
- Publicized
- Online ISSN
- 1745-1345
- DOI
- 10.1587/transcom.E98.B.415
- Type of Manuscript
- PAPER
- Category
- Fundamental Theories for Communications
Authors
Ji-Youp KIM
Seoul National University
Chang-Min CHO
Seoul National University
Wijik LEE
Seoul National University
Jong-Seon NO
Seoul National University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Ji-Youp KIM, Chang-Min CHO, Wijik LEE, Jong-Seon NO, "On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2" in IEICE TRANSACTIONS on Communications,
vol. E98-B, no. 3, pp. 415-421, March 2015, doi: 10.1587/transcom.E98.B.415.
Abstract: Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg { rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $ rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.E98.B.415/_p
Copy
@ARTICLE{e98-b_3_415,
author={Ji-Youp KIM, Chang-Min CHO, Wijik LEE, Jong-Seon NO, },
journal={IEICE TRANSACTIONS on Communications},
title={On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2},
year={2015},
volume={E98-B},
number={3},
pages={415-421},
abstract={Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg { rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $ rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.},
keywords={},
doi={10.1587/transcom.E98.B.415},
ISSN={1745-1345},
month={March},}
Copy
TY - JOUR
TI - On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2
T2 - IEICE TRANSACTIONS on Communications
SP - 415
EP - 421
AU - Ji-Youp KIM
AU - Chang-Min CHO
AU - Wijik LEE
AU - Jong-Seon NO
PY - 2015
DO - 10.1587/transcom.E98.B.415
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E98-B
IS - 3
JA - IEICE TRANSACTIONS on Communications
Y1 - March 2015
AB - Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg { rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $ rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.
ER -
English
