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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
우리는 해당 CDP(Cyclic Difference pair) 측면에서 4단계 상관 관계를 갖는 이진 시퀀스 쌍을 조사합니다. 우리는 순환 차이 쌍의 승수를 정의하고 특정 가상 순환 차이 쌍의 존재 여부를 확인하는 데 적용될 수 있는 승수에 대한 존재 정리를 제시합니다. 그런 다음 모든 역위상 상관 계수가 XNUMX인 이상적인 경우에 중점을 둡니다. 이러한 이상적인 이진 시퀀스 쌍은 길이 υ = XNUMX에 대해 존재하는 것으로 알려져 있습니다.u 모든위한 u ≥ 1. 여기에서 CDP의 승수 이론과 일부 철저한 검색에 대해 개발된 기술을 사용하여 길이 υ ≤ 30에 대해 (1) "다른 것"이 존재하지 않는다는 것을 결정할 수 있습니다. 이상/ 이진 시퀀스 쌍 및 (2) 이 범위의 모든 예는 길이 υ = 4의 예와 동일합니다.u 위에. 이상적인 4레벨 상관 관계를 갖는 이진 시퀀스 쌍이 있는 경우 동위상 상관 관계는 XNUMX가 되어야 한다고 추측합니다. 이는 소위 순환 하다마르 행렬 추측을 의미합니다.
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부
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
부
@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},}
부
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 -