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 of a certain type. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.
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Communicated by G. Korchmaros.
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López, H.H., Rentería-Márquez, C. & Villarreal, R.H. Affine cartesian codes. Des. Codes Cryptogr. 71, 5–19 (2014). https://doi.org/10.1007/s10623-012-9714-2
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DOI: https://doi.org/10.1007/s10623-012-9714-2
Keywords
- Evaluation codes
- Minimum distance
- Complete intersections
- Vanishing ideals
- Degree
- Regularity
- Hilbert function
- Algebraic invariants