The parameters of projective Reed-Mu¨ller codes
Discrete Mathematics
Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Introduction to Coding Theory
Combinatorics, Probability and Computing
Toric Codes over Finite Fields
Applicable Algebra in Engineering, Communication and Computing
Algebraic Geometric Codes: Basic Notions
Algebraic Geometric Codes: Basic Notions
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
Lower bounds on minimal distance of evaluation codes
Applicable Algebra in Engineering, Communication and Computing
The minimum distance of parameterized codes on projective tori
Applicable Algebra in Engineering, Communication and Computing
IEEE Transactions on Information Theory
Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
Finite Fields and Their Applications
Reed-Muller-Type Codes Over the Segre Variety
Finite Fields and Their Applications
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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.