  The environment of NGC1052 has recently attracted much attention because of
the presence of low-surface-brightness galaxies (LSBGs) with apparently
"exotic" properties, making it a region of high interest for the detection of
new objects. We used public deep photometric data from DECaLS to carry out a
comprehensive search for LSBGs over a wide region of 6x6 degrees, equivalent to
2x2 Mpc at the distance of NGC1052. We detected 42 LSBGs with r_e > 5 arcsec
and mu_g(0) > 24 mag/arcsec2, of which 20 are previously undetected objects.
RCP32 stands out with extreme properties: r_e = 23.0 arcsec and mu_g_eff = 28.6
mag/arcsec2, making it one of the lowest surface brightness galaxies ever
detected through integrated photometry, located at just 10 arcmin from the
extensively studied NGC1052-DF2. We explored the presence of GCs in the LSBGs.
We marginally detected a GC system in RCP32, and argue that this LSBG is of
great interest for follow-up observations given its extremely low baryon
density. After analyzing the distribution of galaxies with available
spectroscopy, we identified a large-scale structure of approximately 1 Mpc that
is well isolated in redshift space and centered on NGC1052. The spatial
correlation analysis between the LSBGs and this large-scale structure suggests
their association. However, when exploring the distribution of effective
radius, we find an overpopulation of large LSBGs (r_e > 15 arcsec) located
close to the line of sight of NGC1052. We argue that this is suggestive of a
substructure with similar radial velocity in sight projection, but at a closer
distance, to which some of these apparently larger LSBGs could be associated.
However. possible effects derived from tidal interactions are worthy of further
study. Our work expands the catalog of LSBGs with new interesting objects and
provides a detailed environmental context for the study of LSBGs in this
region.
