Order-Optimal Permutation Codes in the Generalized Cayley Metric

Permutation codes have recently garnered substantial research interest. In this paper, we study the permutation codes in the generalized Cayley metric. The generalized Cayley metric captures the number of generalized transposition errors in a permutation, and subsumes existing 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 construct a new class of permutation codes without interleaving. Our coding scheme, although it is non-constructive, has an order-optimal rate, and in certain circumstances, the rate is higher than that of existing codes based on interleaving.