Constructing Integral Lattices With Prescribed Minimum
نویسنده
چکیده
Methods for computing integral laminated lattices with prescribed minimum are developed. Laminating is a process of stacking layers of an (n l)-dimensional lattice as densely as possible to obtain an «-dimensional lattice. Our side conditions are: All scalar products of lattice vectors are rational integers, and all lattices are generated by vectors of prescribed minimum (square) length m. For m = 3 all such lattices are determined.
منابع مشابه
On Integral Lattices Having an Odd Minimum
We study the kissing number of integral lattices of odd minimum, with special emphasis on the case of minimum 3.
متن کاملComplex and Integral Laminated Lattices
In an earlier paper we studied real laminated lattices (or Z-modules) A„, where A, is the lattice of even integers, and A„ is obtained by stacking layers of a suitable (n — l)-dimensional lattice A„_, as densely as possible, keeping the same minimal norm. The present paper considers two generalizations: (a) complex and quaternionic lattices, obtained by replacing Z-module by /-module, where J m...
متن کاملSpherical Designs from 3 Norm Shell of Integral Lattices
A set of vectors all of which have a constant (non-zero) norm value in a Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Rèseuaux et “designs” sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.
متن کاملCertain Lattice Neighboring from Barnes-wall Lattice and Laminated Lattices
We give classifications of integral lattices which include the Barnes-Wall lattice BW16 or laminated lattices of dimension 1 6 d 6 8 and of minimum 4. Also, we give certain lattice neighboring from each lattice. Furthermore, we study spherical designs and the other properties.
متن کاملSome results on $L$-complete lattices
The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010