There are no Barker arrays having more than two dimensions

Davis, Jedwab and Smith recently proved that there are no 2-dimensional Barker arrays except of size 2?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 ?1 elements. We deduce that there are no Barker arrays having more than two dimensions, as conjectured by Dymond in 1992.

• Type: Conference
• Year: 2007
• Where: DCC
• Authors: Jonathan Jedwab, Matthew G. Parker
• Keywords: 2-dimensional Barker Arrays, Computer Graphics, DCC 2007