Partial permutation decoding for binary linear Hadamard codes

Abstract

Permutation decoding is a technique which involves finding a subset S, called PD-set, 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 2m, for all m≥4 and 1<s≤⌊2m−m−11+m⌋, is described. Moreover, a recursive construction to obtain s-PD-sets of size s+1 for Hm+1 of length 2m+1, from a given s-PD-set of the same size for the Hadamard code of half length Hm is also established.