### 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 v = 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 v ≥ 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 v = 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.

Original language | English |
---|---|

Pages (from-to) | 2266-2271 |

Number of pages | 6 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E93-A |

Issue number | 11 |

DOIs | |

Publication status | Published - 2010 Nov |

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### All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

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*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E93-A, no. 11, pp. 2266-2271. https://doi.org/10.1587/transfun.E93.A.2266

**Binary sequence pairs with two-level correlation and cyclic difference pairs.** / Jin, Seok Yong; Song, Hong Yeop.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Binary sequence pairs with two-level correlation and cyclic difference pairs

AU - Jin, Seok Yong

AU - Song, Hong Yeop

PY - 2010/11

Y1 - 2010/11

N2 - 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 v = 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 v ≥ 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 v = 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.

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 v = 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 v ≥ 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 v = 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.

UR - http://www.scopus.com/inward/record.url?scp=78049525382&partnerID=8YFLogxK

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U2 - 10.1587/transfun.E93.A.2266

DO - 10.1587/transfun.E93.A.2266

M3 - Article

AN - SCOPUS:78049525382

VL - E93-A

SP - 2266

EP - 2271

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 11

ER -