We present details of the construction and characterization of the coaddition of the Sloan Digital Sky Survey Stripe 82 ugriz imaging data. This survey consists of 275 deg$^2$ of repeated scanning by the SDSS camera of $2.5arcdeg$ of $delta$ over $-50arcdeg le alpha le 60arcdeg$ centered on the Celestial Equator. Each piece of sky has $sim 20$ runs contributing and thus reaches $sim2$ magnitudes fainter than the SDSS single pass data, i.e. to $rsim 23.5$ for galaxies. We discuss the image processing of the coaddition, the modeling of the PSF, the calibration, and the production of standard SDSS catalogs. The data have $r$-band median seeing of 1.1arcsec, and are calibrated to $le 1%$. Star color-color, number counts, and psf size vs modelled size plots show the modelling of the PSF is good enough for precision 5-band photometry. Structure in the psf-model vs magnitude plot show minor psf mis-modelling that leads to a region where stars are being mis-classified as galaxies, and this is verified using VVDS spectroscopy. As this is a wide area deep survey there are a variety of uses for the data, including galactic structure, photometric redshift computation, cluster finding and cross wavelength measurements, weak lensing cluster mass calibrations, and cosmic shear measurements.
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