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Binary Sequence Pairs with TwoLevel Correlation and Cyclic Difference Pairs
SeokYong JIN HongYeop SONG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E93A
No.11
pp.22662271 Publication Date: 2010/11/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E93.A.2266
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Signal Design and its Application in Communications) Category: Sequences Keyword: ideal twolevel correlation, cyclic difference pair, cycic Hadamard difference pair, multiplier, circulant Hadamard matrix conjecture,
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Summary:
We investigate binary sequence pairs with twolevel 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 outofphase 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 twolevel correlation then its inphase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.

