Small Golay sequences

We enumerate $H$-phase Golay sequences for $H\le 36$ and lengths up to 33.Our enumeration method is based on filtering by the power spectra.Some of the hexaphase Golay sequence pairs are new. We provide a compact wayto reconstruct all these Golay sequences from specific Golay arrays. The Golay arrays arepart of the three-stage construction introduced by Fiedler, Jedwab, and Parker.All such minimal Golay arrays can be constructed from a small set of Golay sequence pairs withbinary, quaternary, or hexaphase alphabet adjoining 0. We also prove some non-existenceresults for Golay sequences when $H/2$ is odd.