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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.
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