In this paper we prove new lower bounds for the minimum distance of a toric surface code
C_P defined by a convex lattice polygon P⊂R^2. The bounds involve a geometric invariant …

Toric codes are evaluation codes obtained from an integral convex polytope P⊂\mathbbR^n
and finite field \mathbbF_q. They are, in a sense, a natural extension of Reed–Solomon …

We study the Minkowski length L (P) of a lattice polytope P, which is defined to be the largest
number of non-trivial primitive segments whose Minkowski sum lies in P. The Minkowski …

This paper is concerned with the minimum distance computation for higher dimensional toric
codes defined by lattice polytopes in R^n. We show that the minimum distance is …

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 …

We describe two different approaches to making systematic classifications of plane lattice
polygons, and recover the toric codes they generate, over small fields, where these match or …

From an integral convex polytope in ℝ 2 we give an explicit description of an error-correcting
code over the finite field\Bbb F _q of length (q—1) 2. The codes are obtained from toric …

This note presents some new information on how the minimum distance of the generalized
toric code corresponding to a fixed set of integer lattice points S⊂ R 2 varies with the base …

Let $\Lambda $ be a lattice in an $ n $-dimensional Euclidean space $ E $ and let
$\Lambda'$ be a Minkowskian sublattice of $\Lambda $, that is, a sublattice having a basis …

A Reverse Minkowski Theorem Page 1 A Reverse Minkowski Theorem Oded Regev ∗
Courant Institute, New York University New York, New York 10012, United States Noah …