A general criterion to obtain s-PD-sets of minimum size s + 1 for partial permutation decoding, which enable correction up to s errors, for systematic codes over a finite field Fq and Z4-linear codes is provided. We show how this technique can be easily applied to linear cyclic codes over Fq, Z4-linear codes which are the Gray map image of a quaternary linear cyclic code, and some related codes such as quasi-cyclic codes. Furthermore, specific results for some linear and nonlinear binary codes, including simplex, Kerdock, Delsarte-Goethals, and extended dualized Kerdock codes are given. Finally, applying this technique, new s-PD-sets of size s + 1 for Z4-linear Hadamard codes of type 2γ4δ, for all δ ≥ 4 and 1δ- 3; and for Z4-linear simplex codes of type 4m, for all m ≥ 2 and 1m+1- 3, are also provided.

Permutation decoding is a technique that strongly depends on the existence of a special subset, called PD-set, of the permutation automorphism group of a code. In this paper, a general criterion to obtain s-PD-sets of size s + 1, which enable correction up to s errors, for Z4-linear codes is provided. Furthermore, some explicit constructions of s-PD-sets of size s+1 for important families of (nonlinear) Z4-linear codes such as Hadamard and Kerdock codes are given.