Lattice Ideals, Semigroups and Toric Codes

DOI10.1007/978-3-030-40822-0_16zbMath1440.14143OpenAlexW3024151052MaRDI QIDQ5115901

Mesut Şahin

Publication date: 21 August 2020

Published in: Numerical Semigroups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-40822-0_16

zbMATH Keywords

toric varietylinear codenumerical semigrouptoric codelattice idealaffine semigroup

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Research exposition (monographs, survey articles) pertaining to information and communication theory (94-02) Applications to coding theory and cryptography of arithmetic geometry (14G50) Semigroups (20Mxx) Arithmetic rings and other special commutative rings (13Fxx)

Related Items (1)

Calculating the minimum distance of a toric code via algebraic algorithms

Uses Software

• Macaulay2

Cites Work

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• Multigraded Hilbert functions and toric complete intersection codes
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Linkage and codes on complete intersections
• Toric codes and lattice ideals
• Cayley-Bacharach and evaluation codes on complete intersections
• Complete intersection lattice ideals
• Toric complete intersection codes
• Codes over a weighted torus
• Toric codes and finite geometries
• Multigraded regularity: syzygies and fat points
• Uniform bounds on multigraded regularity
• Seven new champion linear codes
• Reed-Muller codes on complete intersections.

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