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On the second generalized Hamming weight of the dual code of a double-error-correcting binary BCH code

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2 Author(s)
Changshik Shim ; Dept. of Electr. & Comput. Eng., State Univ. of New York, Buffalo, NY, USA ; Habong Chung

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

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