Abstract
We define a class of codes that we call affine variety codes. These codes are obtained by evaluating functions in the coordinate ring of an affine variety on all the F_q-rational points of the variety. We show that one can, at least in theory, decode these codes up to half the true minimum distance by using the theory of Grobner bases. We extend results of A. B. Cooper and of X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong.
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