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

Seok Yong Jin, Hong Yeop Song

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 languageEnglish
Pages (from-to)2266-2271
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE93-A
Issue number11
DOIs
Publication statusPublished - 2010 Nov

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Binary sequences
Binary Sequences
Hadamard matrices
Phase Correlation
Multiplier
Circulant Matrix
Hadamard Matrix
Exhaustive Search
Correlation coefficient
Existence Theorem
Nonexistence
Imply
Zero

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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