Perfect N-phase sequences and arrays [spread spectrum communication]

Perfect sequences and arrays have periodic autocorrelation functions whose out-of-phase values are zero. Time-discrete N-phase sequences and arrays have complex elements of magnitude one, and one of (2π/N)n, 0⩽n<N , different phase values. Existence conditions and construction methods for perfect N-phase sequences and arrays with a small alphabet of possible phase values are introduced. Combining the existence conditions with, methods of advanced computer search, new perfect N-phase arrays have been found. The resulting lowest number N of perfect N-phase sequences and arrays up to 40 elements are given in a table, after having applied the construction methods