A brief survey of self-dual codes

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Title: A brief survey of self-dual codes
Author: Oktavia, Rini
Abstract: 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 .
URI: http : / /hdl .handle .net /2152 /ETD -UT -2009 -08 -189
Date: 2010-06-04

Citation

A brief survey of self-dual codes. Master's thesis, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2009 -08 -189 .

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