On the second generalized Hamming weight of the dual code of adouble-error-correcting binary BCH code |
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Authors: | Changshik Shim Habong Chung |
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Affiliation: | Dept. of Electr. & Comput. Eng., State Univ. of New York, Buffalo, NY; |
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Abstract: | 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 |
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