lattice dimension
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Lattice problem — In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central to construction of secure lattice based cryptosystems. For applications in such cryptosystems,… … Wikipedia
Lattice reduction — In mathematics, the goal of lattice basis reduction is given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors. This is realized using different algorithms, whose running time is usually at least exponential … Wikipedia
Lattice constant — The Lattice Constant refers to the constant distance between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a , b , and c . However, in the special case of cubic crystal… … Wikipedia
Lattice problems — In the following computational problems on lattices are described. These problems are essential for lattice based cryptosystems.The Shortest Vector Problem (SVP)In SVP, a basis B of a lattice L is given and one must find the shortest non zero… … Wikipedia
Unimodular lattice — In mathematics, a unimodular lattice is a lattice of discriminant 1 or −1.The E 8 lattice and the Leech lattice are two famous examples. Definitions *A lattice is a free abelian group of finite rank with an integral symmetric bilinear form (·,·) … Wikipedia
Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most … Wikipedia
Niemeier lattice — In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodular lattices of rank 24, which were classified by Hans Volker Niemeier (1973). Venkov (1978) gave a simplified proof of the classification. Witt (1941) has a… … Wikipedia
Coupled map lattice — A coupled map lattice (CML) is a dynamical system that models the behavior of non linear systems (especially partial differential equations). They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems.… … Wikipedia
Leech lattice — In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24 dimensional Euclidean space E24 found by John Leech (1967). Contents 1 History 2 Characterization 3 Properties … Wikipedia
Reciprocal lattice — In physics, the reciprocal lattice of a lattice (usually a Bravais lattice) is the lattice in which the Fourier transform of the spatial function of the original lattice (or direct lattice) is represented. This space is also known as momentum… … Wikipedia
E₈ lattice — In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. The normIn… … Wikipedia
