On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2

Sung-Tai CHOI; Ji-Youp KIM; Jong-Seon NO

doi:10.1587/transcom.E96.B.2190

On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pⁿ+1)/(p^k+1)+(pⁿ-1)/2

Sung-Tai CHOI, Ji-Youp KIM, Jong-Seon NO

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In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pⁿ+1)/(p^k+1)+(pⁿ-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pⁿ-1 is also constructed. The family size of $mathcal{G}$ is pⁿ and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.

Publication: IEICE TRANSACTIONS on Communications Vol.E96-B No.9 pp.2190-2197

Publication Date: 2013/09/01

Publicized

Online ISSN: 1745-1345

DOI: 10.1587/transcom.E96.B.2190

Type of Manuscript: PAPER

Category: Fundamental Theories for Communications

Authors

Sung-Tai CHOI
  Seoul National University
Ji-Youp KIM
  Seoul National University
Jong-Seon NO
  Seoul National University

Keyword

cross-correlation, cyclic code, decimated sequence, exponential sum, m-sequence, sequence family, quadratic form, weight distribution

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Sung-Tai CHOI, Ji-Youp KIM, Jong-Seon NO, "On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2" in IEICE TRANSACTIONS on Communications, vol. E96-B, no. 9, pp. 2190-2197, September 2013, doi: 10.1587/transcom.E96.B.2190.
Abstract: In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pⁿ+1)/(p^k+1)+(pⁿ-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pⁿ-1 is also constructed. The family size of $mathcal{G}$ is pⁿ and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.
URL: https://globals.ieice.org/en_transactions/communications/10.1587/transcom.E96.B.2190/_p

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@ARTICLE{e96-b_9_2190,
author={Sung-Tai CHOI, Ji-Youp KIM, Jong-Seon NO, },
journal={IEICE TRANSACTIONS on Communications},
title={On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2},
year={2013},
volume={E96-B},
number={9},
pages={2190-2197},
abstract={In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pⁿ+1)/(p^k+1)+(pⁿ-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pⁿ-1 is also constructed. The family size of $mathcal{G}$ is pⁿ and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.},
keywords={},
doi={10.1587/transcom.E96.B.2190},
ISSN={1745-1345},
month={September},}

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TY - JOUR
TI - On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2
T2 - IEICE TRANSACTIONS on Communications
SP - 2190
EP - 2197
AU - Sung-Tai CHOI
AU - Ji-Youp KIM
AU - Jong-Seon NO
PY - 2013
DO - 10.1587/transcom.E96.B.2190
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E96-B
IS - 9
JA - IEICE TRANSACTIONS on Communications
Y1 - September 2013
AB - In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pⁿ+1)/(p^k+1)+(pⁿ-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pⁿ-1 is also constructed. The family size of $mathcal{G}$ is pⁿ and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.
ER -