Relative Generalized Hamming Weight Research

Early in 1970s', Wyner invented the models of wiretap channel and wiretap channelof type II. The wiretap channel model composes a sender, a receiver and adversary. Whilein the wiretap channel of type II, the adversary tries to retrieve data bits by tapping anyμtransmitted symbols.The generalized Hamming weight played an important role in coding theory. In thestudy of the wiretap channel of type II, the generalized Hamming weight was extended toa two-code format. Two equivalent concepts of the generalized Hamming weight hierarchyand its two-code format, are the inverse dimension/length profile (IDLP) and the inverserelative dimension/length profile (IRDLP), respectively. In this paper, the relations betweenthe IDLP and the IRDLP are investigated. By using a quotient subcode set, the Singletonbound on the IRDLP is improved by different methods. The new bounds are useful for thestudy of a coordinated two-party wiretap channel of type II.With perspective of the relation of a linear code and its subcode,the relations of trelliscomplexities between them are investigated, which can simplify the NP hard problem to findthe best Ordering of a linear code.