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* Corresponding author 1 GRACE - Geometry, arithmetic, algorithms, codes and encryption Inria Saclay - Ile de France 2 ENSTA ParisTech UMA - Unité de Mathématiques Appliquées

Abstract : We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty-s construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.

Keywords : information set Reed-Muller codes locally correctable codes Index Terms—Locally decodable codes Multiplicity codes





Author: Daniel Augot - Françoise Levy-Dit-Vehel - Man Cuong Ngô -

Source: https://hal.archives-ouvertes.fr/



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