Partial permutation decoding for binary linear and Z4-linear Hadamard codes

Permutation decoding is a technique which involves finding a subset S, called PD-set, of the permutation automorphism group of a code C in order to assist in decoding. A method to obtain s-PD-sets of minimum size s + 1 for partial permutation decoding for binary linear Hadamard codes Hm of length 2 , for all m ≥ 4 and 1 < s ≤ ⌊ 2−m−1 1+m ⌋ , is described. Moreover, a recursive construction to obtain s-PD-sets of size l for Hm+1 of length 2, from a given s-PD-set of the same size for Hm, is also established. These results are generalized to find s-PD-sets for (nonlinear) binary Hadamard codes of length 2, called Z4-linear Hadamard codes, which are obtained as the Gray map image of quaternary linear codes of length 2m−1.