  Permutation codes have recently garnered substantial research interest due to
their potential in various applications including cloud storage systems, genome
resequencing and flash memories. In this paper, we study the theoretical bounds
and constructions of permutation codes in the generalized Cayley metric. The
generalized Cayley metric captures the number of generalized transposition
errors in a permutation, and subsumes previously studied error types, including
transpositions and translocations, without imposing restrictions on the lengths
and positions of the translocated segments. Relying on the breakpoint analysis
proposed by Chee and Vu, we first propose a coding scheme that is order-optimal
albeit not constructive based on this method. We then develop another
construction of permutation codes in the generalized Cayley distance. This
scheme is both explicit and systematic. We also prove the existence of
order-optimal systematic codes and offer a concrete construction based on this
method. For the generalized Cayley metric, we prove that our coding schemes
have less redundancy than the existing codes based on interleaving when the
codelength is sufficiently large and the number of errors is relatively small.
