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arXiv · 1104.0988

Simple proofs for duality of generalized minimum poset weights and weight distributions of (Near-)MDS poset codes

Dae San Kim·Dong Chan Kim·Jong Yoon Hyun
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Abstract

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.

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Dae San Kim, Dong Chan Kim, Jong Yoon Hyun. 2011-04-06. Simple proofs for duality of generalized minimum poset weights and weight distributions of (Near-)MDS poset codes. https://arxiv.org/abs/1104.0988

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