Folding Alternant and Goppa Codes With Non-Trivial Automorphism Groups

@article{Faugre2016FoldingAA,
  title={Folding Alternant and Goppa Codes With Non-Trivial Automorphism Groups},
  author={Jean-Charles Faug{\`e}re and A. Otmani and Ludovic Perret and Fr{\'e}d{\'e}ric de Portzamparc and Jean-Pierre Tillich},
  journal={IEEE Transactions on Information Theory},
  year={2016},
  volume={62},
  pages={184-198}
}
The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non-trivial automorphism group. Such codes display then symmetries allowing compact parity-check or generator matrices. For instance, a key-reduction is obtained by taking quasi-cyclic (QC) or quasi-dyadic (QD) alternant/Goppa codes. We show that the use of such symmetric alternant/Goppa codes… 
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