Parameterized affine codes

Details Parameterized affine codes Parameterized affine codes

2011-09-11

arxiv.org/abs/1109.2353v2

Mathematics

Commutative Algebra

Studia Sci. Math. Hungar., to appear

Scientific paper

Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Groebner bases, to compute the length and the dimension of C_X*(d), the parameterized affine code of degree d on the set X*. If Y is the projective closure of X*, it is shown that C_X^*(d) has the same basic parameters that C_Y(d), the parameterized projective code on the set Y. If X* is an affine torus, we compute the basic parameters of C_X*(d). We show how to compute the vanishing ideals of X* and Y.

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