RT info:eu-repo/semantics/article
T1 Duals of multiplicity codes
A1 Camps Moreno, Eduardo
A1 Fidalgo Díaz, Adrián
A1 López Valdez, Hiram H.
A1 Martínez Peñas, Umberto
A1 Ruano Benito, Diego
A1 San José Rubio, Rodrigo
K1 Teoría de la información
K1 Álgebra
K1 Matemáticas aplicadas
K1 Codificación de datos
K1 Códigos de evaluación
K1 Límite de huella
K1 Códigos de multiplicidad
K1 Códigos polinómicos
K1 Códigos polinómicos ideales
K1 Códigos de Reed-Muller
K1 Códigos de Reed-Solomon
K1 Límite de Schwartz-Zippel
K1 1203 Ciencia de Los Ordenadores
K1 1201 Álgebra
AB Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper, we compute its dimension using Gröbner basis tools, its dual in terms of indicator functions, and explicitly describe a parity-check matrix. In contrast with Reed–Muller, Reed–Solomon, univariate multiplicity, and other evaluation codes, the dual of a multivariate multiplicity code is not equivalent or isometric to a multiplicity code (i.e., this code family is not closed under duality). We use our explicit description to provide a lower bound on the minimum distance for the dual of a multiplicity code.
PB Springer Nature
SN 0925-1022
YR 2026
FD 2026
LK https://uvadoc.uva.es/handle/10324/83961
UL https://uvadoc.uva.es/handle/10324/83961
LA eng
NO Designs, Codes and Cryptography, 2026, vol. 94, n. 4, artículo 81.
NO Producción Científica
DS UVaDOC
RD 09-abr-2026