2026-04-28T19:44:49Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/839612026-04-21T12:44:12Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Camps Moreno, Eduardo Fidalgo Díaz, Adrián López Valdez, Hiram H. Martínez Peñas, Umberto Ruano Benito, Diego San José Rubio, Rodrigo 2026-04-08T07:33:56Z 2026-04-08T07:33:56Z 2026 Designs, Codes and Cryptography, 2026, vol. 94, n. 4, artículo 81. 0925-1022 https://uvadoc.uva.es/handle/10324/83961 10.1007/s10623-026-01812-2 4 Designs, Codes and Cryptography 94 1573-7586 Producción Científica 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. Ministerio de Ciencia e Innovación (MCIN) / Agencia Estatal de Investigación (AEI): PID2022-138906NB-C21 (MCIN/AEI/10.13039/501100011033/ ERDF/EU) National Science Fundation of USA: DMS-2401558 y DMS-2502705. Ministerio de Universidades (MUNI): contrato predoctoral FPU de Rodrigo San José Rubio (FPU20/01311) Open access funding provided by FEDER European Funds and the Junta de Castilla y León under the Research and Innovation Strategy for Smart Specialization (RIS3) of Castilla y León 2021-2027. application/pdf eng Springer Nature info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ © 2026 The Author(s) Atribución 4.0 Internacional Teoría de la información Matemáticas aplicadas Codificación de datos Códigos de evaluación Límite de huella Códigos de multiplicidad Códigos polinómicos Códigos polinómicos ideales Códigos de Reed-Muller Códigos de Reed-Solomon Límite de Schwartz-Zippel 1203 Ciencia de Los Ordenadores 1201 Álgebra Duals of multiplicity codes info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://link.springer.com/article/10.1007/s10623-026-01812-2 SI