Some Upper Bounds on the 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 11, 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 11, the adversary cannot learn more from the illegitimate party. key words: generalized Hamnzing weight, inverse relative dimensionllength projile, quotient subcode set, wiretap channel of type II