Wei’s Duality for Generalized Poset Weight Over Galois Rings

Wei’s duality theorem, proposed by Wei in 1991, initially deals with the generalized Hamming weight (GHW) of linear codes over finite fields. Specifically, the Wei’s duality theorem describes the relationship between the GHWs of a linear code and those of its dual code. The GHWs of linear codes are important parameters for measuring the security of codes in certain cryptographic applications. In this paper, we generalize the concept of GHW of linear codes over finite fields to the generalized poset weight (GPW) of linear codes over Galois rings. We also present an extension of GPW, abbreviated as EGPW. Similar to the GHWs, we derive two forms of the Wei’s duality theorem with respect to GPWs and EGPWs. In conclusion, we demonstrate that the GPWs of linear codes serve as indicators for assessing the security of information transmission within the wire-tap channel of type II .