  Radio searches for extraterrestrial intelligence have mainly targeted the
discovery of narrowband continuous-wave beacons and artificially dispersed
broadband bursts. Periodic pulse trains, in comparison to the above
technosignature morphologies, offer an energetically efficient means of
interstellar transmission. A rotating beacon at the Galactic Center (GC), in
particular, would be highly advantageous for galaxy-wide communications. Here,
we present blipss, a CPU-based open-source software that uses a fast folding
algorithm (FFA) to uncover channel-wide periodic signals in radio dynamic
spectra. Running blipss on 4.5 hours of 4-8 GHz data gathered with the Robert
C. Byrd Green Bank Telescope, we searched the central 6' of our Galaxy for
kHz-wide signals with periods between 11-100 s and duty cycles ($\delta$)
between 10-50%. Our searches, to our knowledge, constitute the first FFA
exploration for periodic alien technosignatures. We report a non-detection of
channel-wide periodic signals in our data. Thus, we constrain the abundance of
4-8 GHz extraterrestrial transmitters of kHz-wide periodic pulsed signals to
fewer than one in about 600,000 stars at the GC above a 7$\sigma$ equivalent
isotropic radiated power of $\approx 2 \times 10^{18}$ W at $\delta \simeq
10\%$. From an astrophysics standpoint, blipss, with its utilization of a
per-channel FFA, can enable the discovery of signals with exotic radio
frequency sweeps departing from the standard cold plasma dispersion law.
