Lower bounds on minimal distance of evaluation codes

DOI10.1007/s00200-009-0102-8zbMath1184.94278OpenAlexW2134475277MaRDI QIDQ843946

Ştefan O. Tohǎneanu

Publication date: 18 January 2010

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-009-0102-8

zbMATH Keywords

Gorenstein ringsyzygiescomplete intersectionevaluation code

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Syzygies, resolutions, complexes and commutative rings (13D02) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (14)

Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ Minimum distance of some evaluation codes ⋮ Parameterized codes over graphs ⋮ Bounding invariants of fat points using a coding theory construction ⋮ The minimum distance of parameterized codes on projective tori ⋮ The minimum distance of sets of points and the minimum socle degree ⋮ Affine Cartesian codes ⋮ Steiner systems and configurations of points ⋮ A commutative algebraic approach to the fitting problem ⋮ Skeleton simplicial evaluation codes ⋮ On the De Boer-Pellikaan method for computing minimum distance ⋮ Minimum distance of linear codes and the \(\alpha\)-invariant ⋮ The Degree and Regularity of Vanishing Ideals of Algebraic Toric Sets Over Finite Fields ⋮ Vanishing Ideals Over Graphs and Even Cycles

Cites Work

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• Gorenstein Algebras and the Cayley-Bacharach Theorem
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• The Geometry of Syzygies
• Cayley-Bacharach theorems and conjectures

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