On the separating redundancy of extended Hamming codes

Haiyang Liu; Daeyeoul Kim; Yan Li; Aaron Z. Jia

doi:10.1109/ISIT.2015.7282887

On the separating redundancy of extended Hamming codes

Haiyang Liu
, Daeyeoul Kim
, Yan Li
, Aaron Z. Jia

Department of Mathematics

CAS - Institute of Microelectronics
National Institute for Mathematical Sciences
China Agricultural University
University of Electronic Science and Technology of China

Research output: Contribution to conference › Conference paper › peer-review

6 Scopus citations

Abstract

Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.

Original language	English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2406-2410
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282887
State	Published - 2015.09.28
Event	2015 IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, China Duration: 2015.06.14 → 2015.06.19

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Conference

Conference	2015 IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	China
City	Hong Kong
Period	15.06.14 → 15.06.19

Keywords

Euclidean geometry
extended Hamming code
integer linear program
Separating matrix
separating redundancy

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10.1109/ISIT.2015.7282887

Cite this

Liu, H., Kim, D., Li, Y., & Jia, A. Z. (2015). On the separating redundancy of extended Hamming codes. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 2406-2410). Article 7282887 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282887

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title = "On the separating redundancy of extended Hamming codes",

abstract = "Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.",

keywords = "Euclidean geometry, extended Hamming code, integer linear program, Separating matrix, separating redundancy",

author = "Haiyang Liu and Daeyeoul Kim and Yan Li and Jia, \{Aaron Z.\}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 2015 IEEE International Symposium on Information Theory, ISIT 2015 ; Conference date: 14-06-2015 Through 19-06-2015",

year = "2015",

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day = "28",

doi = "10.1109/ISIT.2015.7282887",

language = "English",

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Liu, H, Kim, D, Li, Y & Jia, AZ 2015, On the separating redundancy of extended Hamming codes. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282887, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 2406-2410, 2015 IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, China, 15.06.14. https://doi.org/10.1109/ISIT.2015.7282887

On the separating redundancy of extended Hamming codes. / Liu, Haiyang; Kim, Daeyeoul; Li, Yan et al.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2406-2410 7282887 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

Research output: Contribution to conference › Conference paper › peer-review

TY - GEN

T1 - On the separating redundancy of extended Hamming codes

AU - Liu, Haiyang

AU - Kim, Daeyeoul

AU - Li, Yan

AU - Jia, Aaron Z.

PY - 2015/9/28

Y1 - 2015/9/28

N2 - Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.

AB - Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.

KW - Euclidean geometry

KW - extended Hamming code

KW - integer linear program

KW - Separating matrix

KW - separating redundancy

UR - https://www.scopus.com/pages/publications/84969850286

U2 - 10.1109/ISIT.2015.7282887

DO - 10.1109/ISIT.2015.7282887

M3 - Conference paper

AN - SCOPUS:84969850286

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2406

EP - 2410

BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 IEEE International Symposium on Information Theory, ISIT 2015

Y2 - 14 June 2015 through 19 June 2015

ER -

On the separating redundancy of extended Hamming codes

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