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math.AGFeb 14, 2008
39
citations (OpenAlex)
authors
  • Ivan Soprunov
  • Evgenia Soprunova
arXiv abstractPDF
paper

Toric surface codes and Minkowski length of polygons

arXiv:0802.2088 · doi:10.1137/080716554

Abstract

In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily computed for any given P.

18 pages, 9 figures

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  • On Classification of Toric Surface Codes of Low Dimension
  • Classifying toric surface codes of dimension 7
  • On Good Infinite Families of Toric Codes or the Lack Thereof
  • Eventual quasi-linearity of the Minkowski length
  • On parameterised toric codes
  • Toric Codes, Multiplicative Structure and Decoding
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