New Families of <I>p</I>-Ary Sequences of Period $rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude

Wijik LEE; Ji-Youp KIM; Jong-Seon NO

doi:10.1587/transcom.E97.B.2311

New Families of p-Ary Sequences of Period $rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude

Wijik LEE, Ji-Youp KIM, Jong-Seon NO

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Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pⁿ+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.

Publication: IEICE TRANSACTIONS on Communications Vol.E97-B No.11 pp.2311-2315

Publication Date: 2014/11/01

Publicized

Online ISSN: 1745-1345

DOI: 10.1587/transcom.E97.B.2311

Type of Manuscript: PAPER

Category: Fundamental Theories for Communications

Authors

Wijik LEE
  Seoul National University
Ji-Youp KIM
  Seoul National University
Jong-Seon NO
  Seoul National University

Keyword

character, correlation, m-sequences, p-ary sequences, weil bound

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Wijik LEE, Ji-Youp KIM, Jong-Seon NO, "New Families of p-Ary Sequences of Period $rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude" in IEICE TRANSACTIONS on Communications, vol. E97-B, no. 11, pp. 2311-2315, November 2014, doi: 10.1587/transcom.E97.B.2311.
Abstract: Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pⁿ+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.
URL: https://globals.ieice.org/en_transactions/communications/10.1587/transcom.E97.B.2311/_p

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@ARTICLE{e97-b_11_2311,
author={Wijik LEE, Ji-Youp KIM, Jong-Seon NO, },
journal={IEICE TRANSACTIONS on Communications},
title={New Families of p-Ary Sequences of Period $rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude},
year={2014},
volume={E97-B},
number={11},
pages={2311-2315},
abstract={Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pⁿ+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.},
keywords={},
doi={10.1587/transcom.E97.B.2311},
ISSN={1745-1345},
month={November},}

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TY - JOUR
TI - New Families of p-Ary Sequences of Period $rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude
T2 - IEICE TRANSACTIONS on Communications
SP - 2311
EP - 2315
AU - Wijik LEE
AU - Ji-Youp KIM
AU - Jong-Seon NO
PY - 2014
DO - 10.1587/transcom.E97.B.2311
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E97-B
IS - 11
JA - IEICE TRANSACTIONS on Communications
Y1 - November 2014
AB - Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pⁿ+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.
ER -