HP Labs Technical Reports

There is no 2x2x3x3x9 or 4x3x3x9 Perfect Binary Array

Jedwab, Jonathan; Davis, James A.



Abstract: A Perfect binary array (PBA) is an r-dimensional matrix with elements plus or minus 1 such that all out-of-phase periodic autocorrelation coefficients are zero. The smallest sizes for which the existence of a PBA is undecided, 2x2x3x3x9 and 4x3x3x9, are ruled out using computer search and combinatorial argument.

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