Codes from Surfaces with Small Picard Number
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Publication:4564020
DOI10.1137/17M1128277zbMath1409.94942arXiv1803.00486MaRDI QIDQ4564020
John B. Little, Henry K. Schenck
Publication date: 12 June 2018
Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.00486
Vanishing theorems in algebraic geometry (14F17) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)
Related Items
Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces ⋮ Toward good families of codes from towers of surfaces ⋮ Defects of codes from higher dimensional algebraic varieties ⋮ Anticanonical codes from del Pezzo surfaces with Picard rank one ⋮ Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus
Uses Software
Cites Work
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- On the characteristic polynomials of the Frobenius endomorphism for projective curves over finite fields
- Algebraic geometric codes on anticanonical surfaces
- Construction of rational surfaces yielding good codes
- \(K3\) surfaces with Picard number one and infinitely many rational points
- Classification of projective surfaces with small sectional genus: \(\text{char} p\geq 0\)
- The Magma algebra system. I: The user language
- Codes coming from a blowing up of the plane
- On the number of points of algebraic sets over finite fields
- Points on singular Frobenius nonclassical curves
- Error-correcting codes on low rank surfaces
- Classical Algebraic Geometry
- On the Reduction of Points on Abelian Varieties and Tori
- Algebraic geometry codes from higher dimensional varieties
- Weierstrass Points and Curves Over Finite Fields
- On the Picard number of a complex projective variety
- Fundamentals of Error-Correcting Codes
- Minimal cubic surfaces over finite fields
- Toric Surface Codes and Minkowski Length of Polygons
- Toric Surface Codes and Minkowski Sums
- Zeta-functions of conic bundles and of del Pezzo surfaces of degree 4 over finite fields
