Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods

Min Kyu SONG; Hong-Yeop SONG

doi:10.1587/transfun.E102.A.1333

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Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods

Min Kyu SONG, Hong-Yeop SONG

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Summary :

We show that the non-trivial correlation of two properly chosen column sequences of length q-1 from the array structure of two Sidelnikov sequences of periods q^e-1 and q^d-1, respectively, is upper-bounded by $(2d-1)sqrt{q} + 1$, if $2leq e < d < rac{1}{2}(sqrt{q}-rac{2}{sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) imes rac{q^e-1}{q-1}$ with e=2,3,...,d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.10 pp.1333-1339

Publication Date: 2019/10/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E102.A.1333

Type of Manuscript: PAPER

Category: Coding Theory

Authors

Min Kyu SONG
Yonsei University
Hong-Yeop SONG
Yonsei University

Keyword

Sidelnikov sequences, array structure, correlation

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Min Kyu SONG, Hong-Yeop SONG, "Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods" in IEICE TRANSACTIONS on Fundamentals, vol. E102-A, no. 10, pp. 1333-1339, October 2019, doi: 10.1587/transfun.E102.A.1333.
Abstract: We show that the non-trivial correlation of two properly chosen column sequences of length q-1 from the array structure of two Sidelnikov sequences of periods q^e-1 and q^d-1, respectively, is upper-bounded by $(2d-1)sqrt{q} + 1$, if $2leq e < d < rac{1}{2}(sqrt{q}-rac{2}{sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) imes rac{q^e-1}{q-1}$ with e=2,3,...,d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1333/_p

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@ARTICLE{e102-a_10_1333,
author={Min Kyu SONG, Hong-Yeop SONG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods},
year={2019},
volume={E102-A},
number={10},
pages={1333-1339},
abstract={We show that the non-trivial correlation of two properly chosen column sequences of length q-1 from the array structure of two Sidelnikov sequences of periods q^e-1 and q^d-1, respectively, is upper-bounded by $(2d-1)sqrt{q} + 1$, if $2leq e < d < rac{1}{2}(sqrt{q}-rac{2}{sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) imes rac{q^e-1}{q-1}$ with e=2,3,...,d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.},
keywords={},
doi={10.1587/transfun.E102.A.1333},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1333
EP - 1339
AU - Min Kyu SONG
AU - Hong-Yeop SONG
PY - 2019
DO - 10.1587/transfun.E102.A.1333
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2019
AB - We show that the non-trivial correlation of two properly chosen column sequences of length q-1 from the array structure of two Sidelnikov sequences of periods q^e-1 and q^d-1, respectively, is upper-bounded by $(2d-1)sqrt{q} + 1$, if $2leq e < d < rac{1}{2}(sqrt{q}-rac{2}{sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) imes rac{q^e-1}{q-1}$ with e=2,3,...,d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.
ER -