Representing Small Identically Self-Dual Matroids by Self-Dual Codes

نویسندگان

  • Carles Padró
  • Ignacio Gracia
چکیده

The matroid associated to a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated to a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code. This open problem was proposed in [8], where it was proved to be equivalent to an open problem on the complexity of multiplicative linear secret sharing schemes. Some contributions to its solution are given in this paper. A new family of identically self-dual matroids that can be represented by self-dual codes is presented. Besides, we prove that every identically self-dual matroid on at most eight points is representable by a self-dual code.

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عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2005  شماره 

صفحات  -

تاریخ انتشار 2005