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A divide-and-conquer sumcheck protocol
Christophe Levrat, Tanguy Medevielle, Jade Nardi
We present a new sumcheck protocol called Fold-DCS (Fold-Divide-and-Conquer-Sumcheck) for multivariate polynomials based on a divide-and-conquer strategy. Its round complexity and…
Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes
Sarah Bordage, Mathieu Lhotel, Jade Nardi +1
In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code over an algebraic curve is…
Weighted Lifted Codes: Local Correctabilities and Application to Robust Private Information Retrieval
Julien Lavauzelle, Jade Nardi
Low degree Reed-Muller codes are known to satisfy local decoding properties which find applications in private information retrieval (PIR) protocols, for instance. However, their p…
Algebraic Geometric codes on minimal Hirzebruch surfaces
Jade Nardi
We define a linear code by evaluating polynomials of bidegree in the Cox ring on -rational points of the Hirzebruch surface of parameter $η…