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
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2009-08-189 |
| Date | 2009 August 1900 |
| Creators | Oktavia, Rini |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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