2026-04-17T02:18:35Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4802392025-07-29T23:23:05Zcom_2072_98col_2072_378192

urn:hdl:2072/480239 Improving explicit constructions of r-PD-sets for Zps-linear generalized Hadamard codes Rifà i Coma, Josep Torres Martín, Adrián Villanueva, M Permutation decoding PD-set Generalized Hadamard code Zₚs-linear code Generalized Gray map Altres ajuts: acords transformatius de la UAB It is known that Zps -linear codes, which are the Gray map image of Zps -additive codes (linear codes over Zps ), are systematic and a systematic encoding has been found. This makes Zps -linear codes suitable to apply the permutation decoding method, based on the existence of r-PD-sets, which are subsets of the permutation automorphism group of the code. Some constructions of r-PD-sets of minimum size r + 1 for Zps -linear generalized Hadamard codes of type (n;t1, . . . , ts) are known. In this paper, for these codes, we present new constructions of r-PD-sets of size r + 1, which are suitable for all parameters t1, . . . , ts. These allow us to obtain new r-PD-sets for values of r closer to the theoretical upper bound, improving previous known results. 2024 Article Agencia Estatal de Investigación PID2022-137924NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00643 IEEE transactions on information theory ; Vol. 70, Issue 12 (December 2024), p. 8675-8687 open access Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. https://creativecommons.org/licenses/by/4.0/