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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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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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container_title	IEEE transactions on information theory
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creator	JONG YOON HYUN LEE, Yoonjin
description	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.
doi_str_mv	10.1109/TIT.2011.2170111
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source	IEEE Electronic Library (IEL) Journals
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
title	MDS Poset-Codes Satisfying the Asymptotic Gilbert-Varshamov Bound in Hamming Weights
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