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Proof of the Barker array conjecture


Authors: James A. Davis, Jonathan Jedwab and Ken W. Smith
Journal: Proc. Amer. Math. Soc. 135 (2007), 2011-2018
MSC (2000): Primary 05B10; Secondary 94A99
DOI: https://doi.org/10.1090/S0002-9939-07-08703-5
Published electronically: March 2, 2007
MathSciNet review: 2299474
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Abstract: Using only elementary methods, we prove Alquaddoomi and Scholtz's conjecture of 1989, that no $ s \times t$ Barker array having $ s, t > 1$ exists except when $ s = t = 2$.


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Additional Information

James A. Davis
Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
Email: jdavis@richmond.edu

Jonathan Jedwab
Affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6
Email: jed@sfu.ca

Ken W. Smith
Affiliation: Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859
Email: Ken.W.Smith@cmich.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08703-5
Keywords: Barker array, difference set, relative difference set, perfect array, quasiperfect array
Received by editor(s): October 25, 2005
Received by editor(s) in revised form: March 10, 2006
Published electronically: March 2, 2007
Additional Notes: The first author was supported by grant # MDA904-03-1-0032 (NSA)
The second author was supported by grant # 31-611394 (NSERC Canada)
The third author received sabbatical support from Central Michigan University and gracious hospitality from the University of Richmond
Communicated by: John R. Stembridge
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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