Binary phase-manipulated probe signals (BPM, or BPSK) are widely used for echo detection and pulse compression. Reliable detection of the full return time of a long probe requires a sharp matched-filter peak at the correct delay and near-zero responses at other delays. This requirement leads to the synthesis of long binary sequences whose aperiodic autocorrelation has a dominant zero-shift peak and very small sidelobes. We formulate the task as a discrete optimization problem over length N sequences taking values in the set {−1, +1} and propose a practical construction strategy that combines (i) exhaustive enumeration of near-optimal short blocks, (ii) symmetry augmentation (reversal and sign inversion), and (iii) greedy/beam splicing to build long sequences. The method is simple to implement, naturally parallelizable, and improves the normalized sidelobe-energy objective (phi), ISL, and PSL over an optimistic random baseline (best-of-200 trials), while a genetic-algorithm baseline can reach lower ISL at a substantially higher number of objective evaluations.