TY - JOUR
T1 - Affine cartesian codes
AU - López, Hiram H.
AU - Rentería-Márquez, Carlos
AU - Villarreal, Rafael H.
N1 - Funding Information:
Acknowledgments We thank the referees for their careful reading of the paper and for the improvements that they suggested. The second author was supported by COFAA-IPN and SNI. The third author was supported by SNI.
PY - 2014/4
Y1 - 2014/4
N2 - 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.
AB - 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.
KW - Algebraic invariants
KW - Complete intersections
KW - Degree
KW - Evaluation codes
KW - Hilbert function
KW - Minimum distance
KW - Regularity
KW - Vanishing ideals
UR - http://www.scopus.com/inward/record.url?scp=84894679725&partnerID=8YFLogxK
U2 - 10.1007/s10623-012-9714-2
DO - 10.1007/s10623-012-9714-2
M3 - Artículo
SN - 0925-1022
VL - 71
SP - 5
EP - 19
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1
ER -