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

Title
Simple proofs for duality of generalized minimum poset weights and weight distributions of (Near-) MDS poset codes
Authors
Kim D.S.Kim D.C.Hyun J.Y.
Ewha Authors
현종윤
SCOPUS Author ID
현종윤scopus
Issue Date
2012
Journal Title
Advanced Studies in Contemporary Mathematics (Kyungshang)
ISSN
1229-3067JCR Link
Citation
vol. 22, no. 1, pp. 145 - 152
Indexed
SCOPUS; KCI scopus
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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연구기관 > 수리과학연구소 > Journal papers
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