Lattice polytopes in coding theory

Abstract

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 bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.

Keywords

• Toric code, Lattice polytope, Minkowski length, Sparse polynomials

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