2026-04-13T03:00:04Zhttps://recercat.cat/oai/request

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

00925njm 22002777a 4500 dc Rifà i Coma, Josep author Torres Martín, Adrián author Villanueva, M author 2024 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. Permutation decoding PD-set Generalized Hadamard code Zₚs-linear code Generalized Gray map Improving explicit constructions of r-PD-sets for Zps-linear generalized Hadamard codes