An Algorithmic
    Reduction
    Theory for
   Binary Codes:         An Algorithmic Reduction Theory for
   LLL and more
     Thomas                       Binary Codes: LLL and more
  Debris-Alazard,
    Léo Ducas,
  Wessel P.J. van
     Woerden
 Lattice Reduction       Thomas Debris-Alazard, Léo Ducas, Wessel P.J. van Woerden
  Introduction
  An Invariant: GSO
  LLL Algorithm
 Code Reduction
  Orthopodality
  Babai Algorithm for
  Codes
  LLL Reduction and
  LLL Algorithm for
  Binary Code
  Griesmer’s Bound
  versus LLL
                                                                                                             1/50
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Avery good reference to learn about lattices
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        https:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     //homepages.cwi.nl/~dadush/teaching/lattices-2018/
  An Algorithmic
    Reduction
    Theory for
   Binary Codes:                                                         This work
   LLL and more
     Thomas
  Debris-Alazard,
    Léo Ducas,
  Wessel P.J. van    Analogies (definition, proposition, theorem) from Lattices to Codes
     Woerden                             via an algorithmic approach (LLL)
 Lattice Reduction
  Introduction
  An Invariant: GSO
  LLL Algorithm     Wepropose a reduction theory for codes (LLL-reduced bases):
 Code Reduction
  Orthopodality       1. Proof of bound on codes (Griesmer...)
  Babai Algorithm for
  Codes               2. Use to speed-up cryptanalytic algorithms
  LLL Reduction and
  LLL Algorithm for
  Binary Code
  Griesmer’s Bound
  versus LLL
                                                                                                        2/50
  An Algorithmic
    Reduction
    Theory for
   Binary Codes:                                                         This work
   LLL and more
     Thomas
  Debris-Alazard,
    Léo Ducas,
  Wessel P.J. van    Analogies (definition, proposition, theorem) from Lattices to Codes
     Woerden                             via an algorithmic approach (LLL)
 Lattice Reduction
  Introduction
  An Invariant: GSO
  LLL Algorithm     Wepropose a reduction theory for codes (LLL-reduced bases):
 Code Reduction
  Orthopodality       1. Proof of bound on codes (Griesmer...)
  Babai Algorithm for
  Codes               2. Use to speed-up cryptanalytic algorithms
  LLL Reduction and
  LLL Algorithm for
  Binary Code
  Griesmer’s Bound
  versus LLL
                                   Avery good reference to learn about lattices
                                                          https:
                       //homepages.cwi.nl/~dadush/teaching/lattices-2018/
                                                                                                        2/50
  An Algorithmic
    Reduction
    Theory for
   Binary Codes:
   LLL and more
     Thomas       1 Lattice Reduction
  Debris-Alazard,
    Léo Ducas,           Introduction
  Wessel P.J. van
    Woerden              An Invariant: GSO
 Lattice Reduction       LLL Algorithm
  Introduction
  An Invariant: GSO
  LLL Algorithm
 Code Reduction
  Orthopodality   2 Code Reduction
  Babai Algorithm for
  Codes                  Orthopodality
  LLL Reduction and
  LLL Algorithm for      Babai Algorithm for Codes
  Binary Code
  Griesmer’s Bound
  versus LLL             LLL Reduction and LLL Algorithm for Binary Code
                         Griesmer’s Bound versus LLL
                                                                                                    3/50