Abstract
A new class of permutation codes is presented where,
instead of considering one permutation as a codeword, codewords
consist of a sequence of permutations. The advantage of using
permutations, i.e. their favourable symbol diversity properties,
is preserved. Additionally, using sequences of permutations
as codewords, code rates close to the optimum rate can be
achieved. Firstly, the complete set of permutations is divided
into subsets by using set partitioning. Binary data is then
mapped to permutations from these subsets. These permutations,
together with a parity permutation, will form the codeword. Two
constructions will be presented: one capable of detecting and
correcting substitution errors and the other capable of detecting
and correcting either substitution or deletion errors.