The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
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114
Nous montrons que la corrélation non triviale de deux séquences de colonnes de longueur correctement choisies q-1 à partir de la structure matricielle de deux séquences Sidelnikov de périodes qe-1 et qd-1, respectivement, est limité supérieur par $(2d-1)sqrt{q} + 1$, si $2leq e < d < rac{1}{2}(sqrt{q}- rac{2}{sqrt {q}}+1)$. Sur cette base, nous proposons une construction en combinant des colonnes correctement choisies à partir de tableaux de taille $(q-1) imes rac{q^e-1}{q-1}$ avec e=2,3,...,d. Le processus de combinaison élargit la taille de la famille tout en maintenant la limite supérieure de la corrélation maximale non triviale. Nous proposons également un algorithme pour générer la famille de séquences basé sur le théorème des restes chinois. L’algorithme proposé est plus efficace que l’approche par force brute.
Min Kyu SONG
Yonsei University
Hong-Yeop SONG
Yonsei University
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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 qe-1 and qd-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 qe-1 and qd-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 qe-1 and qd-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 -