Duality and Support Weight Distributions

Schaathun, Hans Georg

doi:10.1109/tit.2004.826673

Cited by 9 publications

(2 citation statements)

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“…Barg and Purkayastha in [1], as in the case of Wei's original proof in [12], do not adopt the matroid theory and exploit instead parity check and generator matrices for linear codes. The authors in [8] adopt the geometric formulation of the generalized minimum Hamming weights for projective systems in [11] and use multi-set techniques, originated from [5] and [10], in order to extend the proofs in [11,Theorem 4.1] to the case of generalized minimum poset weights. So their proof is far different from the original proof of Wei in [12].…”

Section: Introductionmentioning

confidence: 99%

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

Ким¹,

Kim²,

Hyun³

2011

Preprint

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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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Section: Introductionmentioning

confidence: 99%

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

Ким¹,

Kim²,

Hyun³

2011

Preprint

View full text Add to dashboard Cite

show abstract

“…From the SWD of a single code, they were able to determine the weight distribution of a corresponding infinite class of codes. After the introduction of the related weight hierarchy in [2], this problem received renewed interest, and in recent years, the SWD's of particular codes [3], [4] and dual codes [5]- [7] have been studied. In this correspondence, we give a short and simple calculation of the second SWD of the Kasami codes.…”

Section: Introductionmentioning

confidence: 99%