On the Second Generalized Hamming Weight of the Dual Code of a Double-Error-Correcting Binary BCH Code

초록

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 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. In this correspondence, the second generalized Hamming weight of the dual code of a double-error-correcting BCH code is derived and we prove that except for m=4, the second generalized Hamming weight of [2m −1. 2m]-dual BCH codes achieves the Griesmer bound. © 1995 IEEE

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