Some new bounds on relative generalized Hamming weight
Zhuojun Zhuang, Yuan Luo, A. J. Han Vinck, Bin Dai · 2011
The relative generalized Hamming weight (RGHW) of a linear code and a linear subcode, a two-code extension of generalized Hamming weight (GHW), has been applied to the wiretap channel of type II. The concept has also been extended in the wiretap network II for the secrecy control of linear network coding. In trellis-based decoding algorithms, a given subcode provides additional information to measure the decoding complexity. Bounds on RGHW facilitate the design of optimal schemes for the above applications. The only known explicit bound on RGHW was the generalized Singleton bound. In this paper, we show some important inequalities with respect to RGHW and then introduce three new bounds, the generalized Plotkin and Griesmer bounds as well as the relative constant-weight (RCW) bound. The relations among the new bounds and the Singleton one are simply discussed.