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On the Concatenated Structure of a Linear Code

  • Nicolas Sendrier

Abstract

We address here the problem of finding a concatenated structure in a linear code ? given by its generating matrix, that is, if ? is equivalent to the concatenation of an inner code B0 and an outer code E0, then find two codes B and E such that their concatenation is equivalent to ?. If the concatenated structure exists and is non trivial (i.e. the inner code B is non trivial), the dual distance of ? is equal to the dual distance of B. If this dual distance is small enough to allow the computation of many small weight words in the dual of ?, it is possible to recover first an inner code B, then an outer code E whose concatenation is equivalent to ?. These two codes are equivalent respectively to the original inner and outer codes B0 and E0.

Key wordsConcatenated codes, Code equivalence, McEliece cryptosystem, Niederreiter cryptosystem. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Nicolas Sendrier
    • 1
  1. 1.Projet CODES, INRIA, Domaine de Voluceau, Rocquencourt, BP 105, F-78153 Le Chesnay CEDEX, FranceFR

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