Partial permutation decoding for binary linear Hadamard codes

Permutation decoding is a technique which involves finding a subset S, called PDset, of the permutation automorphism group PAut(C) of a code C in order to assist in decoding. A method to obtain s-PD-sets of size s + 1 for partial permutation decoding for the binary linear Hadamard codes Hm of length 2 m, for all m ≥ 4 and 1 < s ≤ b(2m −m− 1)/(1 + m)c, is described. Moreover, a recursive construction to obtain s-PD-sets of size s+ 1 for Hm+1 of length 2 m+1, from a given s-PD-set of the same size for the Hadamard code of half length Hm is also established.