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

Abstract

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.