Improving Explicit Constructions of r-PD-Sets for Zs-Linear Generalized Hadamard Codes

Abstract

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.