2025/05/20 by Eduardo Camps-Moreno, Adrián Fidalgo-Díaz, Moreno, Eduardo Camps +14 · 1 voice
Computer Science · Engineering · Mathematics · #Advanced Mathematical Theories #Cellular Automata and Applications #Coding theory and cryptography #graph theory and CDMA systems
paper · pdf · doi:10.1007/s10623-026-01812-2
openalex publication_date 2026/01/01 · openalex created_date 2026/04/08 · openalex updated_date 2026/07/02
Abstract 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.