Binary phase shaping, contrast ratio, and merit

We construct and study $+1/-1$ sequences that mimic randomly produced sequences. The pseudorandomness property discussed here is aperiodic autocorrelation — a random sequence typically has low correlation with truncated versions of itself. Golay's merit factor is a single parameter describing the autocorrelation quality of a sequence. The sequences we discuss are all constructed using the Legendre symbol on finite fields pf prime order. Our interest came from a problem in chemical instrumentation.