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Generalized Hamming weights for linear codes

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1 Author(s)
Wei, V.K. ; Bellcore, Morristown, NJ, USA

Motivated by cryptographical applications, the algebraic structure, of linear codes from a new perspective is studied. By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained. These weights characterize the code performance on the wire-tap channel of type II. Basic properties of generalized weights are derived, the values of these weights for well-known classes of codes are determined, and lower bounds on code parameters are obtained. Several open problems are also listed

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 5 )