Improving Explicit Constructions of r-PD-Sets for Zₚs-Linear Generalized Hadamard Codes
Year: 2024
Type: article
Abstract: It is known that$\mathbb {Z}_{p^{s}}$-linear codes, which are the Gray map image of$\mathbb {Z}_{p^{s}}$-additive codes (linear codes over$\mathbb {Z}_{p^{s}}$), are systematic and a systematic encoding has been found. This makes$\mathbb {Z}_{p^{s}}$-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$\mathbb {Z}_{p^{s}}$-linear generalized Hadamard codes of type$(n;t_{1}, {\dots },t_{s})$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$t_{1}, {\dots },t_{s}$. These allow us to obtain new r-PD-sets for values of r closer to the theoretical upper bound, improving previous known results.
Institution: Universitat Autònoma de Barcelona
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,495
OpenAlex ID: W4401749640