Partial permutation decoding for binary linear and -linear Hadamard codes

In this paper, s--sets of minimum size for partial permutation decoding for the binary linear Hadamard code of length , for all and , are constructed. Moreover, recursive constructions to obtain s--sets of size for of length , from an s--set of the same size for , are also described. These results are generalized to find s--sets for the -linear Hadamard codes of length , , which are binary Hadamard codes (not necessarily linear) obtained as the Gray map image of quaternary linear codes of type . Specifically, s-PD-sets of minimum size for , for all and , are constructed and recursive constructions are described.