Welcome to the resource topic for 2005/194
Title:
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
Authors: Ryutaroh Matsumoto, Kaoru Kurosawa, Toshiya Itoh, Toshimitsu Konno, Tomohiko Uyematsu
Abstract:Let N(d,d^\perp) denote the minimum
length n of a linear code C with d and d^{\bot},
where d is the minimum Hamming distance of C
and
d^{\bot} is the minimum Hamming distance of C^{\bot}.
In this paper,
we show a lower bound and an upper bound on N(d,d^\perp).
Further,
for small values of d and d^\perp, we determine
N(d,d^\perp) 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.
ePrint: https://eprint.iacr.org/2005/194
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