Minkowski's theorem 1 Minimum Distance

Comparing Lattice Families for Bounded Distance Decoding near ...

An upper bound on λ1(L) is given by Minkowski's first Theorem. Theorem 1 (Minkowski's First Theorem). For any full-rank lattice L of rank n ...

Minkowski's successive minima in convex and discrete ge

Actually, in [62] Minkowski proved Theorem 1.1 as an inequality relating the volume of K and the minimal norm of a non-trivial lattice point, ...

Limits of the Minkowski distance as related to the generalized mean

I'm pretty sure this "norm" is infinite for every set of vectors →x=(x1,...,xn), →y=(y1,...,yn) which have at least two distinct (non-equal ...

Minkowski's Theorem

If the set in question is compact, the restriction to the volume can be weak- ened to “at least 1” from “greater than 1”. ... show range v ⊆ B 0 1.

Minkowski Distance - an overview | ScienceDirect Topics

In the standard Euclidean metric, we know that the circle centered at (0,0) is all points where d2(x,0) + d2(y,0) = 1. For the general Minkowski metric, the ...

Modifying Minkowski's Theorem - PAUL R. SCOTT - UNI-Lj

0 1988 Academic Press, Inc. 1. INY~R~DUCTI~N. Let ,4 be a lattice in n-dimensional space E”, having ...

How to Calculate Minkowski Distance in R? - GeeksforGeeks

Let us consider a 2-dimensional space having three points P1 (X1, Y1), P2 (X2, Y2), and P3 (X3, Y3), the Minkowski distance is given by ( |X1 – ...

Minimal requirements for Minkowski's theorem in the plane I

Finally, let E be the convex hull of the three points. (±t, -l) and (0, 1/t) where t > 1 . The triangle E is admissible, and has only one chord of symmetry ...

Number Balancing is as hard as Minkowski's Theorem and Shortest ...

Finding the minimum, however, is NP-hard. In polynomial time,the differencing algorithm by Karmarkar and Karp from 1982 can produce a solution ...

Lattice (List) Decoding Near Minkowski's Inequality - IEEE Xplore

Our primary contribution is a polynomial-time algorithm that list decodes this family to distances approaching 1/\sqrt {2} of the minimum ...

Lattices and the Geometry of Numbers - OSF

... Minkowski's Lattice Point Theorem or Minkowski's Convex Body Theorem as ... least 1/2𝜆𝑛 distance from 𝑥 i.e the covering radius is at least greater than 1/2𝜆𝑛 ...

On the Minkowski distances and products of sum sets

Given two points p, q in the real plane, the signed area of the rectangle with the diagonal [pq] equals the square of the Minkowski distance ...

An extension of Minkowski's theorem and its applications to ...

Minkowski's Theorem asserts that every centered measure on the sphere which is not concentrated on a great subsphere is the surface area ...

[2010.04809] Lattice (List) Decoding Near Minkowski's Inequality

Our primary contribution is a polynomial-time algorithm that list decodes this family to distances approaching 1/\sqrt{2} of the minimum distance.

An Analogue to Minkowski's Geometry of Numbers in a Field of Series

(1) F(X(1') = arl) is the minimum of F(X) in all lattice points X $ 0, and ... 1, and to this body correspond by the theorem n minima T(1), T(2) ... T ...

the distance function from the boundary in a minkowski space

We shall see that the Minkowski distance from S satisfies ρ(DδS(x)) = 1 for almost every x ∈ A := Rn \ S (see Proposition 3.3(i), and Theorem ...

A BRUNN-MINKOWSKI THEORY FOR MINIMAL SURFACES

catenoid among minimal hedgehogs are given. 1. Introduction and statement of results. The set Kn+1 of convex bodies of the (n+1)-Euclidean vector space Rn+1 is.

geometry of numbers with applications to number theory

Abstract Blichfeldt and Minkowski. 152. References. 154. 1. Lattices in Euclidean Space ... that q is positive definite with minimum 1. Namely, plugging in. (x ...

Minkowski's Convex Body Theorem and Integer Programming - jstor

... 1, then Jo <- minimum such j, else jo - n. 8. BASIS +- {b, b2, ..., bo_l ... 1/2 = M (say) on the distance between any bo and its closest lattice point ...

Minimal requirements for Minkowski's theorem in the plane II

Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice.