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The generalized Hamming weight of a linear code is a new notion of higher dimensional Hamming weights. Let C be an [n,k] linear code and D be a subcode. The support of D is the cardinality of the set of not-always-zero bit positions of D. The rth generalized Hamming weight of C, denoted by dr(C), is defined as the minimum support of an r-dimensional subcode of C. It was shown by Wei (1991) that the generalized Hamming weight hierarchy of a linear code completely characterizes the performance of the code on the type II wire-tap channel defined by Ozarow and Wyner (1984). In the present paper the second generalized Hamming weight of the dual code of a double-error-correcting BCH code is derived and the authors prove that except for m=4, the second generalized Hamming weight of [2m-1, 2m]-dual BCH codes achieves the Griesmer bound
Published in:
Information Theory, IEEE Transactions on
(Volume:41
,
Issue:
3
)
Date of Publication: May 1995
- Page(s):
- 805 - 808
- ISSN :
- 0018-9448
- INSPEC Accession Number:
- 4959152
- Digital Object Identifier :
- 10.1109/18.382030
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 06 August 2002
- Issue Date :
- May 1995
- Sponsored by :
- IEEE Information Theory Society
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