Barker Arrays I: Even Number of Elements

A Barker array is a two-dimensional array with elements $ \pm 1$ such that all out-of-phase aperiodic autocorrelation coefficients are $0,1$, or $ - 1$. No $s \times t$ Barker array with $s,t > 1$ and $( s,t ) \ne ( 2,2 )$ is known, and it is conjectured that none exists. A class of arrays that includes Barker arrays is defined. Nonexistence results for this class of arrays in the case $st$ even, providing support for the Barker array conjecture, are proved. Several connections, in the case $st$ even, between this class of arrays and perfect, quasi-perfect, and doubly quasi-perfect binary arrays are demonstrated.