Affine cartesian codes

Abstract

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. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.

Designs, Codes and Cryptography, to appear

References in corpus (2)

• Parameterized affine codes
• The minimum distance of parameterized codes on projective tori

Cited by in corpus (17)

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• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes
• Relative generalized Hamming weights of evaluation codes
• Indicator functions, v-numbers and Gorenstein rings in the theory of projective Reed-Muller-type codes
• A repair scheme for a distributed storage system based on multivariate polynomials
• Affine Cartesian codes with complementary duals
• Erasures repair for decreasing monomial-Cartesian and augmented Reed-Muller codes of high rate
• The dual of an evaluation code
• Minimum distance functions of complete intersections
• Complete intersection vanishing ideals on sets of clutter type over finite fields