2011/04/06 by Dae San Kim, Kim, Dae San, Dong Chan Kim +3
Computer Science · Engineering · Mathematics · #05B35 #94B99 #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT #msc:05B35 #msc:94B99
paper · pdf · doi:10.48550/arxiv.1104.0988
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arxiv created 2011/04/06 · openalex publication_date 2011/04/06 · arxiv updated 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.