Parameterized affine codes
Hiram H. Lopez, Eliseo Sarmiento, Maria Vaz Pinto, Rafael H., Villarreal
TL;DR
This paper introduces an algebraic method using Groebner bases to compute parameters of parameterized affine codes on affine algebraic toric sets, linking affine and projective codes and providing explicit calculations for affine tori.
Contribution
It presents a novel algebraic approach to determine the length and dimension of parameterized affine codes using Groebner bases, and relates affine and projective code parameters.
Findings
Provides a method to compute length and dimension of affine codes.
Shows the equivalence of parameters between affine and projective codes.
Calculates parameters for affine tori.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.