Information sets of Multiplicity codes

  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)},
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. 
Fast systematic encoding of multiplicity codes
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  • 2016
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Information sets and partial permutation decoding for codes from finite geometries
List-Decoding Multiplicity Codes
It is shown that univariate multiplicity codes of rate R over fields of prime order can be list-decoded from a (1 R e) fraction of errors in polynomial time (for constant R;e).
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New generalizations of the Reed-Muller codes-I: Primitive codes
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New generalizations of the Reed-Muller codes-II: Nonprimitive codes
  • E. Weldon
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1968
A class of nonprimitive cyclic codes quite similar in structure to the original Reed-Muller codes is presented, and it is shown that for given values of code length and rate the codes have relatively large minimum distances.
High-rate codes with sublinear-time decoding
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Enumerative combinatorics
This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
List-decoding multiplicity codes,” Electronic Colloquium on Computational Complexity (ECCC)
  • vol. TR12-044,
  • 2012