Quotient Subcode Set and Inverse Relative Dimension/Length Profile

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 relations between the IDLP and the IRDLP are investigated. By using a quotient subcode set, the Singleton bound on the IRDLP is improved by different methods. The new bounds are useful for the study of a coordinated two-party wiretap channel of type II.