Generalized Hamming weights of linear codes

The generalized Hamming weight, d/sub r/(C), of a binary linear code C is the size of the smallest support of any r-dimensional subcode of C. The parameter d/sub r/(C) determines the code's performance on the wire-tap channel of Type II. Bounds on d/sub r/(C), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d/sub r/(C) is presented and examples are given of codes meeting this bound with equality.<
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