Lattice polytopes in coding theory

zbMath1348.14074arXiv1411.0028MaRDI QIDQ307910

Ivan Soprunov

Publication date: 5 September 2016

Published in: Journal of Algebra, Combinatorics, Discrete Structures and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0028

zbMATH Keywords

lattice polytopeMinkowski lengthtoric code

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Applications to coding theory and cryptography of arithmetic geometry (14G50) Combinatorial codes (94B25)

Related Items

$\mathbb{F}_q$-Zeros of Sparse Trivariate Polynomials and Toric 3-Fold Codes, Secret sharing schemes with strong multiplication and a large number of players from toric varieties, Unnamed Item, Evaluation codes and their basic parameters, The dual of an evaluation code, Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes

Uses Software

• Magma
• Code Tables

Cites Work

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• On the parameters of \(r\)-dimensional toric codes
• Seven new champion linear codes
• Toric Surface Codes and Minkowski Length of Polygons
• Dual Toric Codes and Polytopes of Degree One
• Bringing Toric Codes to the Next Dimension
• Toric Surface Codes and Minkowski Sums