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TitleParameterized affine codes.
Author(s) Hiram H. López, Maria Vaz Pinto, Eliseo Sarmiento, Rafael H. Villarreal
TypeArticle in Journal
AbstractLet 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.
KeywordsPrimary 13P25, Secondary 14G50, 14G15, 11T71, 94B27, 94B05, Evaluation codes, parameterized affine codes, vanishing ideals, minimum distance, dimension, length, affine Hilbert function
ISSN0081-6906; 1588-2896/e
URL http://www.akademiai.com/doi/abs/10.1556/SScMath.49.2012.3.1216
LanguageEnglish
JournalStud. Sci. Math. Hung.
Volume49
Number3
Pages406--418
PublisherAkad
Year2012
Edition0
Translation No
Refereed No
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