PARTIAL PERMUTATION DECODING FOR SIMPLEX CODES
We show how to find s-PD-sets of size s + 1 that satisfy the Gordon-Schonheim bound for partial permutation decoding for the binary simplex codes S-n(F-2) for all n >= 4, and for all values of s up to left perpendicular2(n)-1/nright perpendicular - 1. The construction also applies to the q-ary simplex codes S-n(F-q) for q > 2, and to s-antiblocking information systems of size s + 1, for s up to left perpendicular(q(n)-1)/(q-1)/nright perpendicular - 1 for all q.
permutation decoding simplex codes hamming codes antiblocking decoding