منابع مشابه
Lattice polytopes in coding theory
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations. 2010 MSC: 14M25, 14G50,...
متن کاملLattice Points in Lattice Polytopes
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry with respect to P is at most 8d · (8l+7)2d+1. If, moreover,P is a simplex, then this bound can be improved to 8 · (8l+ 7)d+1.As an application, we deduce new upper bounds on the volume ofa lattice polytope, given its ...
متن کاملLattice Polytopes in Algebra ,
[1] Victor V. Batyrev and Benjamin Nill. Multiples of lattice polytopes without interior lattice points. Moscow Mathematical Journal 7:195–207, 2007. [2] Victor V. Batyrev, Benjamin Nill. Combinatorial aspects of mirror symmetry. Contemporary Mathematics, 452:35–66, 2008. [3] Barbara Baumeister, Christian Haase, Benjamin Nill and Andreas Paffenholz. On permutation polytopes. Advances in Mathema...
متن کاملLattice Points inside Lattice Polytopes
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩ lZ (provided it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d · (8l+7) 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 9 · (8l+ 7) d+1 . This implies that the maximum volume of a lattice polytope P ⊂ R d containing exactly k ≥ 1 points of lZ in its interior, is...
متن کاملLattice Points in Simple Polytopes
P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and Pukhlikov [8] (valid for lattice polytopes such that the primitive vectors on edges through each vertex of P form a basis of the lattice). As a corollary, we recover results of Pommersheim [9] and ...
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ژورنال
عنوان ژورنال: Journal of Algebra Combinatorics Discrete Structures and Applications
سال: 2015
ISSN: 2148-838X
DOI: 10.13069/jacodesmath.75353