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 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 it 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.
inverse relative dimension/length profile generalized hamming weight wiretap channel of type ii quotient subcode set