A brief survey of self-dual codes

This report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights of self-dual binary codes using the extremal weight enumerator formula. We describe the shadow code o...

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Bibliographic Details
Main Author:	Oktavia, Rini
Format:	Others
Language:	English
Published:	2010
Subjects:	Self-Dual Codes Weight Enumerator MacWilliams Identity Gleason's Theorem on Self-Dual Codes Minimum Distance
Online Access:	http://hdl.handle.net/2152/ETD-UT-2009-08-189

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spelling	ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2009-08-1892015-09-20T16:53:47ZA brief survey of self-dual codesOktavia, RiniSelf-Dual CodesWeight EnumeratorMacWilliams IdentityGleason's Theorem on Self-Dual CodesMinimum DistanceThis report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights of self-dual binary codes using the extremal weight enumerator formula. We describe the shadow code of a self-dual code and the restrictions of the weight enumerator of the shadow code. Then using the restrictions, we calculate the weight enumerators of self-dual codes of length 38 and 40 and we obtain the known weight enumerators of this lengths. Finally, we investigate the Gaborit-Otmani experimental construction of selfdual binary codes. This construction involves a fixed orthogonal matrix, and we compare the result to the results obtained using other orthogonal matrices.text2010-06-04T14:43:28Z2010-06-04T14:43:28Z2009-082010-06-04T14:43:28ZAugust 2009thesisapplication/pdfhttp://hdl.handle.net/2152/ETD-UT-2009-08-189eng
collection	NDLTD
language	English
format	Others
sources	NDLTD
topic	Self-Dual Codes Weight Enumerator MacWilliams Identity Gleason's Theorem on Self-Dual Codes Minimum Distance
spellingShingle	Self-Dual Codes Weight Enumerator MacWilliams Identity Gleason's Theorem on Self-Dual Codes Minimum Distance Oktavia, Rini A brief survey of self-dual codes
description	This report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights of self-dual binary codes using the extremal weight enumerator formula. We describe the shadow code of a self-dual code and the restrictions of the weight enumerator of the shadow code. Then using the restrictions, we calculate the weight enumerators of self-dual codes of length 38 and 40 and we obtain the known weight enumerators of this lengths. Finally, we investigate the Gaborit-Otmani experimental construction of selfdual binary codes. This construction involves a fixed orthogonal matrix, and we compare the result to the results obtained using other orthogonal matrices. === text
author	Oktavia, Rini
author_facet	Oktavia, Rini
author_sort	Oktavia, Rini
title	A brief survey of self-dual codes
title_short	A brief survey of self-dual codes
title_full	A brief survey of self-dual codes
title_fullStr	A brief survey of self-dual codes
title_full_unstemmed	A brief survey of self-dual codes
title_sort	brief survey of self-dual codes
publishDate	2010
url	http://hdl.handle.net/2152/ETD-UT-2009-08-189
work_keys_str_mv	AT oktaviarini abriefsurveyofselfdualcodes AT oktaviarini briefsurveyofselfdualcodes
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A brief survey of self-dual codes

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