In 1991, Wei introduced generalized minimum Hamming weights for linear codes and showed their monotonicity and duality. Recently, several authors extended these results to the case of generalized minimum poset weights by using different methods. Here, we would like to prove the duality by using matroid theory. This gives yet another and very simple proof of it. In particular, our argument will make it clear that the duality follows from the well-known relation between the rank function and the corank function of a matroid. In addition, we derive the weight distributions of linear MDS and Near-MDS poset codes in the same spirit.
Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach
Fudan University（复旦大学）；National and Local Joint Laboratory of Cyberspace Security Technology（网络空间安全技术国家地方联合工程实验室）；Yiwu Research Institute of Fudan University（复旦大学义乌研究院）；The University of Hong Kong（香港大学）
Some structural properties of mixed orthogonal arrays and their irredundancy
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；Faculty of Engineering and Natural Sciences, Sabancı University（萨班奇大学工程与自然科学学院）
