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Primal-Dual Distance Bounds of Linear Codes With Application to Cryptography
Matsumoto, R.; Kurosawa, K.; Itoh, T.; Konno, T.; Uyematsu, T.;
Information Theory, IEEE Transactions on
Volume 52,
Issue 9,
Sept. 2006
Page(s):4251
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4256
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
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