Reference : On basis vectors of lattices
E-prints/Working papers : First made available on ORBilu
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45087
On basis vectors of lattices
English
Barthel, Jim Jean-Pierre mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS) >]
Müller, Volker mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS) >]
Undated
No
[en] Lattices ; Basis vectors ; Dirichlet's theorem on arithmetic progressions
[en] Integer lattices enjoy increasing interest among mathematicians and cryptographers. However, there are still many elementary open questions, like finding specific vectors or particular bases of a given lattice. Our study consists in exhibiting which integer vectors may be chosen as basis vectors of a chosen lattice. The compelling part of our development is that this condition is obtained through an unusual application of Dirichlet's Theorem on primes in arithmetic progressions and that it has a surprising consequence for vectors achieving the successive minima.
http://hdl.handle.net/10993/45087

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