Abstract:In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code C = C(C, P, D) is a vector space associated to evaluations on P of functions in the Riemann-Roch space L C (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 codeword of C. AG codes are good candidates to construct short proof systems, but there exists no eff… Show more
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