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Electronic Colloquium on Computational Complexity

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All reports by Author Jade Nardi:

TR21-118 | 11th August 2021
Daniel Augot, Sarah Bordage, Jade Nardi

Efficient multivariate low-degree tests via interactive oracle proofs of proximity for polynomial codes

We consider the proximity testing problem for error-correcting codes which consist in evaluations of multivariate polynomials either of bounded individual degree or bounded total degree. Namely, given an
oracle function $f : L^m \rightarrow \mathbb F_q$, where $L\subset \mathbb F_q$, a verifier distinguishes whether $f$ is the evaluation of a ... more >>>

TR20-165 | 6th November 2020
Sarah Bordage, Jade Nardi

Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes

Revisions: 2

In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code $C = C(\mathcal C, \mathcal P, D)$ is a vector space associated to evaluations on $\mathcal P$ of functions in the Riemann-Roch space $L_\mathcal C(D)$. The problem of testing proximity to an ... more >>>

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