Information sets of Multiplicity codes

@article{Augot2015InformationSO,
  title={Information sets of Multiplicity codes},
  author={Daniel Augot and Françoise Levy-dit-Vehel and Man Cuong Ng{\^o}},
  journal={2015 IEEE International Symposium on Information Theory (ISIT)},
  year={2015},
  pages={2401-2405}
}
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 Kopparty. 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. 
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