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
Nous étudions les paires de séquences binaires avec une corrélation à deux niveaux en termes de paires de différences cycliques (CDP) correspondantes. Nous définissons les multiplicateurs d'une paire de différences cycliques et présentons un théorème d'existence pour les multiplicateurs, qui pourrait être appliqué pour vérifier l'existence/non-existence de certaines paires de différences cycliques hypothétiques. Ensuite, nous nous concentrons sur le cas idéal où tous les coefficients de corrélation déphasés sont nuls. On sait qu’une telle paire de séquences binaires idéale existe pour une longueur υ = 4u pour chaque u ≥ 1. En utilisant les techniques développées ici sur la théorie des multiplicateurs d'un CDP et une recherche exhaustive, nous pouvons déterminer que, pour des longueurs υ ≤ 30, (1) il n'existe "aucun autre" idéal/ paire de séquences binaires et (2) chaque exemple dans cette plage est équivalent à celui de longueur υ = 4u au-dessus de. Nous conjecturons que s'il existe une paire de séquences binaires avec une corrélation idéale à deux niveaux, alors sa corrélation en phase doit être de 4. Cela implique ce qu'on appelle la conjecture de la matrice Hadamard circulante.
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Seok-Yong JIN, Hong-Yeop SONG, "Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 11, pp. 2266-2271, November 2010, doi: 10.1587/transfun.E93.A.2266.
Abstract: We investigate binary sequence pairs with two-level correlation in terms of their corresponding cyclic difference pairs (CDPs). We define multipliers of a cyclic difference pair and present an existence theorem for multipliers, which could be applied to check the existence/nonexistence of certain hypothetical cyclic difference pairs. Then, we focus on the ideal case where all the out-of-phase correlation coefficients are zero. It is known that such an ideal binary sequence pair exists for length υ = 4u for every u ≥ 1. Using the techniques developed here on the theory of multipliers of a CDP and some exhaustive search, we are able to determine that, for lengths υ ≤ 30, (1) there does not exist "any other" ideal/ binary sequence pair and (2) every example in this range is equivalent to the one of length υ = 4u above. We conjecture that if there is a binary sequence pair with an ideal two-level correlation then its in-phase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.2266/_p
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@ARTICLE{e93-a_11_2266,
author={Seok-Yong JIN, Hong-Yeop SONG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs},
year={2010},
volume={E93-A},
number={11},
pages={2266-2271},
abstract={We investigate binary sequence pairs with two-level correlation in terms of their corresponding cyclic difference pairs (CDPs). We define multipliers of a cyclic difference pair and present an existence theorem for multipliers, which could be applied to check the existence/nonexistence of certain hypothetical cyclic difference pairs. Then, we focus on the ideal case where all the out-of-phase correlation coefficients are zero. It is known that such an ideal binary sequence pair exists for length υ = 4u for every u ≥ 1. Using the techniques developed here on the theory of multipliers of a CDP and some exhaustive search, we are able to determine that, for lengths υ ≤ 30, (1) there does not exist "any other" ideal/ binary sequence pair and (2) every example in this range is equivalent to the one of length υ = 4u above. We conjecture that if there is a binary sequence pair with an ideal two-level correlation then its in-phase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.},
keywords={},
doi={10.1587/transfun.E93.A.2266},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2266
EP - 2271
AU - Seok-Yong JIN
AU - Hong-Yeop SONG
PY - 2010
DO - 10.1587/transfun.E93.A.2266
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2010
AB - We investigate binary sequence pairs with two-level correlation in terms of their corresponding cyclic difference pairs (CDPs). We define multipliers of a cyclic difference pair and present an existence theorem for multipliers, which could be applied to check the existence/nonexistence of certain hypothetical cyclic difference pairs. Then, we focus on the ideal case where all the out-of-phase correlation coefficients are zero. It is known that such an ideal binary sequence pair exists for length υ = 4u for every u ≥ 1. Using the techniques developed here on the theory of multipliers of a CDP and some exhaustive search, we are able to determine that, for lengths υ ≤ 30, (1) there does not exist "any other" ideal/ binary sequence pair and (2) every example in this range is equivalent to the one of length υ = 4u above. We conjecture that if there is a binary sequence pair with an ideal two-level correlation then its in-phase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.
ER -