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Zbl 1033.94019
Hansen, Søren Have
Error-correcting codes from higher-dimensional varieties. (English)
[J] Finite Fields Appl. 7, No. 4, 530-552 (2001). ISSN 1071-5797

The author generalizes the well-known construction of Goppa codes associated to curves over finite fields to higher-dimensional varieties. The Riemann-Roch theorem, used to estimate the parameters of the codes, is replaced by intersection theory. The author applies his method to certain Deligne-Lusztig surfaces, to Hermitian hypersurfaces and to certain ruled surfaces. The parameters of the codes he constructs are rather good. In some instances they meet the Griesmer bound.
[René Schoof (Roma)]

MSC 2000:: *94B27 Geometric methods in coding theory
14G50 Applications of algebraic geometry to coding theory
94B65 Bounds on codes
14C17 Intersection theory

Keywords: intersection theory; Deligne-Lusztig surfaces; Hermitian hypersurface; ruled surfaces; Griesmer bound

Cited in: Zbl 1073.94025

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