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Affine cartesian codes

2012; Springer Nature; Volume: 71; Issue: 1 Linguagem: Inglês

10.1007/s10623-012-9714-2

1573-7586

Hiram H. López, Carlos Rentería-Márquez, Rafael H. Villarreal,

Commutative Algebra and Its Applications

We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters of a certain type. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.