Wiretap lattice codes from number fields with no small norm elements

• Main Authors: Ong, Soon Sheng, Oggier, Frédérique
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics::Recreational mathematics
• Online Access: https://hdl.handle.net/10356/103869; http://hdl.handle.net/10220/19314
• Institution: Nanyang Technological University

We consider the problem of designing reliable and con dential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for nite lattice constellations a nite sum of inverse of algebraic norms, in fact the analogous for nite sums of the known criterion for in nite constellations, which motivates us to study totally real number elds with few elements of small norms, over which ideal lattices can be built to provide wiretap lattice codes. More precisely, we rst narrow down our search to abelian number elds known to provide reliable lattice codes, among which we look for no small inert primes and large regulators.