On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2

Ji-Youp KIM; Chang-Min CHO; Wijik LEE; Jong-Seon NO

doi:10.1587/transcom.E98.B.415

On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4p^n/2-2

Ji-Youp KIM, Chang-Min CHO, Wijik LEE, Jong-Seon NO

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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 4p^n/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 p^m ≠ 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

correlation, decimation, m-sequences, p-ary sequences, sequence family

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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 4p^n/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 p^m ≠ 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://globals.ieice.org/en_transactions/communications/10.1587/transcom.E98.B.415/_p

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@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 4p^n/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 p^m ≠ 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},}

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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 4p^n/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 p^m ≠ 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 -