  The aim of this study is to search for quasi-periodical structures at
moderate cosmological redshifts $z \la 0.5 $. We mainly use the SDSS DR7 data
on the luminous red galaxies (LRGs) with redshifts $0.16 \leq z \leq 0.47$. At
first, we analyze features (peaks) in the power spectra of radial (shell-like)
distributions using separate angular sectors in the sky and calculate the power
spectra within each sector. As a result, we found some signs of a large-scale
anisotropic quasi-periodic structure detectable through 6 sectors out of a
total of 144 sectors. These sectors are distinguished by large amplitudes of
dominant peaks in their radial power spectra at wavenumbers $k$ within a narrow
interval of $0.05 < k < 0.07$~h~Mpc$^{-1}$. Then, passing from a spherical
coordinate system to a Cartesian one, we found a special direction such that
the total distribution of LRG projections on it contains a significant
($\ga$5$\sigma$) quasi-periodical component. We assume that we are dealing with
a signature of a quasi-regular structure with a characteristic scale $116 \pm
10$~h$^{-1}$~Mpc. Our assumption is confirmed by a preliminary analysis of the
SDSS DR12 data.
