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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Toric Complete Intersection Codes, Ivan Soprunov
Toric Complete Intersection Codes, Ivan Soprunov
Mathematics and Statistics Faculty Publications
In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.
Bringing Toric Codes To The Next Dimension, Ivan Soprunov, Jenya Soprunova
Bringing Toric Codes To The Next Dimension, Ivan Soprunov, Jenya Soprunova
Mathematics and Statistics Faculty Publications
This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes in $\mathbb{R}^n$. We show that the minimum distance is multiplicative with respect to taking the product of polytopes, and behaves in a simple way when one builds a k-dilate of a pyramid over a polytope. This allows us to construct a large class of examples of higher dimensional toric codes where we can compute the minimum distance explicitly.
Toric Surface Codes And Minkowski Length Of Polygons, Ivan Soprunov, Jenya Soprunova
Toric Surface Codes And Minkowski Length Of Polygons, Ivan Soprunov, Jenya Soprunova
Mathematics and Statistics Faculty Publications
In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.