We show that computing the approximate length of the shortest vector in a lattice within a factor c is NP-hard for randomized reductions for any constant c < p 2. We also give a deterministic reduction based on a number theoretic conjecture.

The statistical properties of the error in uniform scalar quantization have been analyzed by a number of authors in the past, and is a well understood topic today. The analysis has also been extended to the case of dithered quantizers, and the advantages and limitations of dithering have been studied and well documented in the literature. Lattice vector quantization is a natural extension into ...

A vector difference calculus is developed for physical models defined on a general triangulating graph G, which may be a regular or an extremely irregular lattice, using discrete field quantities roughly analogous to differential forms. The role of the space L of p-forms at a point is taken on by the linear space generated at a graph vertex by the geometrical p-simplices which contain it. The v...

Every Dedekind complete Riesz space X has a unique sup-completion s , which is lattice cone. This paper aims to present systematic study this cone by extending several known results the general setting, proving new and, in particular, introducing for elements of finite and infinite parts. enables us get satisfactory abstract formulation some classical setting spaces. We prove, version Borel-Can...

We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme.