The generalized Hamming weight played an important role in coding theory. In the study of the wiretap channel of type II, the generalized Hamming weight was extended to a two-code format. Two equivalent concepts of the generalized Hamming weight hierarchy and its two-code format, are the inverse dimension/length profile (IDLP) and the inverse relative dimension/length profile (IRDLP), respectively. In this paper, the Singleton upper bound on the IRDLP is improved by using a quotient subcode set and a subset with respect to a generator matrix, respectively. If these new upper bounds on the IRDLP are achieved, in the corresponding coordinated two-party wire-tap channel of type II, the adversary cannot learn more from the illegitimate party.

This letter reveals that whole link reciprocity does not exist in general amplify-and-forward (AF) time division duplex (TDD) relay systems due to the gain matrix. To resolve this problem, a novel gain matrix design method is proposed. Any existing gain matrix design criterion can be adopted in the downlink (uplink) to ensure optimal performance, and the proposed scheme is used in the uplink (downlink), with small adjustment, to keep whole link reciprocity. Simulation results show that, the proposed method can maintain whole link reciprocity without performance loss.