The dual minimum distance of arbitrary-dimensional algebraic-geometric codes
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Publication:420711
DOI10.1016/j.jalgebra.2011.09.030zbMath1241.14014arXiv0905.2345OpenAlexW1516340542MaRDI QIDQ420711
Publication date: 23 May 2012
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.2345
Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Divisors, linear systems, invertible sheaves (14C20)
Related Items (26)
On the dual minimum distance and minimum weight of codes from a quotient of the Hermitian curve ⋮ Hermitian codes from higher degree places ⋮ The dual geometry of Hermitian two-point codes ⋮ Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve ⋮ On the Hermitian curve and its intersections with some conics ⋮ Rational points on cubic surfaces and AG codes from the norm-trace curve ⋮ On the geometry of Hermitian one-point codes ⋮ Minimum-weight codewords of the Hermitian codes are supported on complete intersections ⋮ Real and complex rank for real symmetric tensors with low ranks ⋮ On the weights of dual codes arising from the GK curve ⋮ Minimal codewords in norm-trace codes ⋮ Finite subsets of projective spaces with bad postulation in a fixed degree ⋮ Differential codes on higher dimensional varieties via Grothendieck's residue symbol ⋮ Sets computing the symmetric tensor rank ⋮ On the gonality sequence of smooth curves ⋮ Lower bounds on the minimum distance in Hermitian one-point differential codes ⋮ Generalized Hamming weights of codes obtained from smooth plane curves ⋮ A zero-dimensional approach to Hermitian codes ⋮ On the small-weight codewords of some Hermitian codes ⋮ Locally recoverable codes correcting many erasures over small fields ⋮ Intersections between the norm-trace curve and some low degree curves ⋮ Weight distribution of Hermitian codes and matrices rank ⋮ Codes over a weighted torus ⋮ Rank 1 decompositions of symmetric tensors outside a fixed support ⋮ Hermitian codes and complete intersections ⋮ Dependent subsets of embedded projective varieties
Cites Work
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- Algebraic function fields and codes
- Sums of residues on algebraic surfaces and application to coding theory
- Error-correcting codes on low rank surfaces
- Projective reed-muller codes
- Cayley-Bacharach theorems and conjectures
- Lectures on Curves on an Algebraic Surface. (AM-59)
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