There are no Barker arrays having more than two dimensions

Authors:
Jonathan Jedwab;Matthew G. Parker
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, Canada V5A 1S6;Department of Informatics, High Technology Center in Bergen, University of Bergen, Bergen, Norway 5020
Venue:
Designs, Codes and Cryptography
Year:
2007

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Abstract

Davis, Jedwab and Smith recently proved that there are no 2-dimensional Barker arrays except of size 2 脳 2. We show that the existence of a (d + 1)-dimensional Barker array implies the existence of a d-dimensional Barker array with the same number of 卤 1 elements. We deduce that there are no Barker arrays having more than two dimensions, as conjectured by Dymond in 1992.