Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes. (arXiv:2011.04295v4 [cs.IT] UPDATED)

In this work, we initiate the study of proximity testing to Algebraic
Geometry (AG) codes. An AG code $C = C(\mathcal{X}, \mathcal{P}, D)$ over an
algebraic curve $\mathcal{X}$ is a vector space associated to evaluations on
$\mathcal{P}$ of functions in the Riemann-Roch space $L_\mathcal{X}(D)$. The
problem of testing proximity to an error-correcting code $C$ consists in
distinguishing between the case where an input word, given as an oracle,
belongs to $C$ and the one where it is far from every …

geometry oracle