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  • 1 Centro de Investigacifion y de Estudios Avanzados del IPN Departamento de Matemfiaticas Apartado Postal 14-740 07000 Mexico City, D.F. Mexico
  • 2 Universidade Técnica de Lisboa Departamento de Matemfiatica, Instituto Superior Tecnico Avenida Rovisco Pais, 1 1049-001 Lisboa Portugal
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Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Gröbner bases, to compute the length and the dimension of CX* (d), the parameterized affine code of degree d on the set X*. If Y is the projective closure of X*, it is shown that CX* (d) has the same basic parameters that CY (d), the parameterized projective code on the set Y. If X* is an affine torus, we compute the basic parameters of CX* (d). We show how to compute the vanishing ideals of X* and Y.

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