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." />


Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs

Seok-Yong JIN  Hong-Yeop SONG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.11   pp.2266-2271
Publication Date: 2010/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.2266
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and its Application in Communications)
Category: Sequences
Keyword: 
ideal two-level correlation,  cyclic difference pair,  cycic Hadamard difference pair,  multiplier,  circulant Hadamard matrix conjecture,  

Full Text: PDF>>
Buy this Article




Summary: 
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.