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SUMMARY:Leo Ducas (CWI Amsterdam)
DTSTART:20200603T150000Z
DTEND:20200603T160000Z
DTSTAMP:20260423T035615Z
UID:CANTA/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANTA/2/">An
  Algorithmic Reduction Theory for Binary Codes</a>\nby Leo Ducas (CWI Amst
 erdam) as part of Royal Holloway CANTA-Launch\n\n\nAbstract\nJoint work (i
 n Progress) with\nThomas Debris-Alazard and Wessel van Woerden\n\nLattice 
 reduction is the task of finding a basis of short and somewhat orthogonal 
 vectors of a given lattice. In 1985 Lenstra\, Lenstra and Lovasz proposed 
 a polynomial time algorithm for this task\, with an application to factori
 ng rational polynomials. Since then\, the LLL algorithm has found countles
 s application in algorithmic number theory and in cryptanalysis.\n\nThere 
 are many analogies to be drawn between Euclidean lattices and linear codes
  over finite fields. In this work\, we propose to extend the range of thes
 e analogies by considering the task of reducing the basis of a binary code
 . In fact\, all it takes is to choose the adequate notion mimicking Euclid
 ean orthogonality (namely orthopodality)\, after which\, all the required 
 notions\, arguments\, and algorithms unfold before us\, in quasi-perfect a
 nalogy with lattices.\n
LOCATION:https://researchseminars.org/talk/CANTA/2/
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