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

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2011-12, Vol.57 (12), p.8021-8026
Main Authors: JONG YOON HYUN, LEE, Yoonjin
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic methods
Asymptotic properties
Chains
Codes
Coding, codes
Construction
Decomposition
Exact sciences and technology
Gilbert-Varshamov bound
Hamming weight
Information theory
Information, signal and communications theory
Interpolation
Mathematical analysis
MDS poset-code
Measurement
poset-isometry
poset-metric
Signal and communications theory
Space vehicles
Telecommunications and information theory
Theorems
Upper bound
{\cal N}{\cal R}{\cal T} -metric
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2170111