International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Ryutaroh Matsumoto

Publications

Year
Venue
Title
2015
EPRINT
2014
EPRINT
2005
EPRINT
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
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.