Primal-Dual Distance Bounds of Linear Codes With Application to Cryptography

  • Authors:

  • R. Matsumoto;K. Kurosawa;T. Itoh;T. Konno;T. Uyematsu

  • Affiliations:

  • Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol.;-;-;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

Let N(d,dperp) denote the minimum length n of a linear code C with d and dperp, where d is the minimum Hamming distance of C and dperp is the minimum Hamming distance of Cperp. In this correspondence, we show lower bounds and an upper bound on N(d,dperp). Further, for small values of d and dperp, we determine N(d,dperp) and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa et al