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In 1991, Wei introduced generalized minimum Hamming weights for linear codesand showed their monotonicity and duality. Recently, several authors extendedthese results to the case of generalized minimum poset weights by usingdifferent methods. Here, we would like to prove the duality by using matroidtheory. This gives yet another and very simple proof of it. In particular, ourargument will make it clear that the duality follows from the well-knownrelation between the rank function and the corank function of a matroid. Inaddition, we derive the weight distributions of linear MDS and Near-MDS posetcodes in the same spirit.

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