The dual minimum distance of arbitrary dimensional algebraic--geometric codes

Abstract In this article, the minimum distance of the dual C ⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field F q is studied. The approach is based on problems a la Cayley–Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m . If X is a curve, the result improves in some situations the well-known Goppa designed distance .

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