New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences

Young-Sik KIM; Ji-Woong JANG; Sang-Hyo KIM; Jong-Seon NO

doi:10.1587/transfun.E96.A.1872

New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences

Young-Sik KIM, Ji-Woong JANG, Sang-Hyo KIM, Jong-Seon NO

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In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field F_q which is the splitting field of x^2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.9 pp.1872-1882

Publication Date: 2013/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E96.A.1872

Type of Manuscript: PAPER

Category: Spread Spectrum Technologies and Applications

Authors

Young-Sik KIM
  Chosun University
Ji-Woong JANG
  Ulsan College
Sang-Hyo KIM
  Sungkyunkwan University
Jong-Seon NO
  Seoul National University

Keyword

autocorrelation, ideal autocorrelation, legendre sequences, quaternary sequences, sequences

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Young-Sik KIM, Ji-Woong JANG, Sang-Hyo KIM, Jong-Seon NO, "New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences" in IEICE TRANSACTIONS on Fundamentals, vol. E96-A, no. 9, pp. 1872-1882, September 2013, doi: 10.1587/transfun.E96.A.1872.
Abstract: In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field F_q which is the splitting field of x^2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1872/_p

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@ARTICLE{e96-a_9_1872,
author={Young-Sik KIM, Ji-Woong JANG, Sang-Hyo KIM, Jong-Seon NO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences},
year={2013},
volume={E96-A},
number={9},
pages={1872-1882},
abstract={In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field F_q which is the splitting field of x^2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.},
keywords={},
doi={10.1587/transfun.E96.A.1872},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1872
EP - 1882
AU - Young-Sik KIM
AU - Ji-Woong JANG
AU - Sang-Hyo KIM
AU - Jong-Seon NO
PY - 2013
DO - 10.1587/transfun.E96.A.1872
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2013
AB - In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field F_q which is the splitting field of x^2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.
ER -