MDS poset-codes satisfying the asymptotic Gilbert-Varshamov bound in hamming weights

Jong Yoon Hyun; Yoonjin Lee

doi:10.1109/TIT.2011.2170111

MDS poset-codes satisfying the asymptotic Gilbert-Varshamov bound in hamming weights

Jong Yoon Hyun, Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Article number	6094282
Pages (from-to)	8021-8026
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	57
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2011.2170111
State	Published - Dec 2011

Bibliographical note

Funding Information:
Manuscript received January 07, 2010; revised March 07, 2011; accepted May 25, 2011. Date of current version December 07, 2011. J. Y. Hyun and Y. Lee were supported in part by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2009-0093827). Y. Lee was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MEST) (No. 2011-0015684).

Keywords

Gilbert-Varshamov bound
MDS poset-code
NRT-metric
poset-isometry
poset-metric

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10.1109/TIT.2011.2170111

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title = "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.",

keywords = "Gilbert-Varshamov bound, MDS poset-code, NRT-metric, poset-isometry, poset-metric",

author = "Hyun, {Jong Yoon} and Yoonjin Lee",

note = "Funding Information: Manuscript received January 07, 2010; revised March 07, 2011; accepted May 25, 2011. Date of current version December 07, 2011. J. Y. Hyun and Y. Lee were supported in part by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2009-0093827). Y. Lee was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MEST) (No. 2011-0015684).",

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doi = "10.1109/TIT.2011.2170111",

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MDS poset-codes satisfying the asymptotic Gilbert-Varshamov bound in hamming weights

Abstract

Bibliographical note

Keywords

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