Generalizing the passage from a fan to a toric variety, we provide a combinatorial approach to construct arbitrary effective torus actions on normal, algebraic varieties. Based on the notion of a… Expand

Intersection theory is used to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension.Expand

Applicable Algebra in Engineering, Communication and Computing

2002

TLDR

This work treats Hirzebruch surfaces and an explicit construction of an error-correcting code of length (q-1)2 over the finite field 𝔽q, obtained by evaluation of rational functions on a toric surface associated to the polytope.Expand

Error correcting codes are defined and important parameters for a code are explained. Parameters of new codes constructed on algebraic surfaces are studied. In particular, codes resulting from… Expand

We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach… Expand

Upper and lower bounds on the minimum distance of a toric code constructed from a polygon $P \subset {\mathbb R}^2$ are obtained by examining Minkowski sum decompositions of subpolygons of $P$.Expand

New lower bounds for the minimum distance of a toric surface code $\mathcal{C}_P$ defined by a convex lattice polygon using the full Minkowski length of P is proved.Expand