PD-sets for Z4-linear codes: Hadamard and Kerdock codes

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.