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Wiretap lattice codes from number fields with no small norm elements. (English) Zbl 1335.94106
Summary: We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields with few elements of small norms, over which ideal lattices can be built to provide wiretap lattice codes. More precisely, we first narrow down our search to Abelian number fields known to provide reliable lattice codes, among which we look for no small inert primes and large regulators.

94B60 Other types of codes
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
11Y16 Number-theoretic algorithms; complexity
Full Text: DOI
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