Abstract
We construct new families of smooth projective curves over a finite field F/sub q/ with a lot of F/sub q/-rational points. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Let X be a smooth projective curve of genus g=g(X) defined over a finite field F/sub q/. The Goppa construction of linear [n,k,d]/sub q/-codes associated to the curve X is described.
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