Seven new champion linear codes

DOI10.1112/S1461157013000041zbMath1311.14027arXiv1212.5197OpenAlexW2098086440MaRDI QIDQ5169594

Gavin D. Brown, Alexander M. Kasprzyk

Publication date: 11 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5197

zbMATH Keywords

linear codeslattice polygonstoric codes

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) Linear codes (general theory) (94B05) Combinatorial aspects of matroids and geometric lattices (05B35) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

Lattice polytopes in coding theory ⋮ Toric codes and finite geometries ⋮ $\mathbb{F}_q$-Zeros of Sparse Trivariate Polynomials and Toric 3-Fold Codes ⋮ Rational points of lattice ideals on a toric variety and toric codes ⋮ On parameterized toric codes ⋮ Calculating the minimum distance of a toric code via algebraic algorithms ⋮ Lattice Ideals, Semigroups and Toric Codes ⋮ Remarks on generalized toric codes ⋮ On classification of toric surface codes of low dimension ⋮ Projective toric codes

Uses Software

• Magma
• Graded Ring Database

Cites Work

• On the structure of generalized toric codes
• On toric codes and multivariate Vandermonde matrices
• The Magma algebra system. I: The user language
• Small polygons and toric codes