  This article aims to explore the bridge between the algebraic structure of a
linear code and the complete decoding process. To this end, we associate a
specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code. The
binomials involved in the reduced Gr\"obner basis of such an ideal relative to
a degree-compatible ordering induce a uniquely defined test-set for the code,
and this allows the description of a Hamming metric decoding procedure.
Moreover, the binomials involved in the Graver basis of $I_+(\mathcal C)$
provide a universal test-set which turns out to be a set containing the set of
codewords of minimal support of the code.
