Quotient Subcode Set and Inverse Relative Dimension/Length Profile

Abstract

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.