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Abstract We present a catalog of 5598 ultra-diffuse galaxy (UDG) candidates with effective radiusr_e> 5.″3 distributed throughout the southern portion of the DESI Legacy Imaging Survey covering ∼15,000 deg². The catalog is most complete for physically large (r_e> 2.5 kpc) UDGs lying in the redshift range 1800 ≲cz/km s⁻¹≲ 7000, where the lower bound is defined by where incompleteness becomes significant for large objects on the sky and the upper bound by our minimum angular size selection criterion. Because physical size is integral to the definition of a UDG, we develop a method of distance estimation using existing redshift surveys. With three different galaxy samples, two of which contain UDGs with spectroscopic redshifts, we estimate that the method has a redshift accuracy of ∼75% when the method converges, although larger, more representative spectroscopic UDG samples are needed in order to fully understand the behavior of the method. We are able to estimate distances for 1079 of our UDG candidates (19%). Finally, to illustrate some uses of the catalog, we present both distance-independent and distance-dependent results. In the latter category, we establish that the red sequence of UDGs lies on the extrapolation of the red sequence relation for bright ellipticals and that the environment–color relation is at least qualitatively similar to that of high surface brightness galaxies. Both of these results challenge some of the models proposed for UDG evolution.