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MDS Poset-Codes Satisfying the Asymptotic Gilbert–Varshamov Bound in Hamming Weights

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2 Author(s)
Jong Yoon Hyun ; Inst. of Math. Sci., Seoul, South Korea ; Yoonjin Lee

We prove that MDS linear poset-codes satisfy Gilbert-Varshamov bound for their Hamming weights asymptotically. We also construct MDS linear poset-codes on arbitrary poset-metric spaces by using the Dilworth's chain decomposition theorem and results about the Hermite interpolation problem over a finite field. We prove that there exist linear poset-codes with large weights for both poset-metrics and Hamming metrics, as well.

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Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 12 )