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

R. Matsumoto,K. Kurosawa,T. Itoh,Toshimitsu Konno,T. Uyematsu

Published 2005 in IEEE Transactions on Information Theory

ABSTRACT

Let N(d,d<sup>perp</sup>) denote the minimum length n of a linear code C with d and d<sup>perp</sup>, where d is the minimum Hamming distance of C and d<sup>perp</sup> is the minimum Hamming distance of C<sup>perp</sup>. In this correspondence, we show lower bounds and an upper bound on N(d,d<sup>perp</sup>). Further, for small values of d and d<sup>perp</sup>, we determine N(d,d<sup>perp</sup>) 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

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