CryptoDB
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
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| 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. |
BibTeX
@misc{eprint-2005-12530,
title={Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography},
booktitle={IACR Eprint archive},
keywords={foundations / boolean function, linear code},
url={http://eprint.iacr.org/2005/194},
note={ ryutaroh@it.ss.titech.ac.jp 13311 received 24 Jun 2005, last revised 12 Jun 2006},
author={Ryutaroh Matsumoto and Kaoru Kurosawa and Toshiya Itoh and Toshimitsu Konno and Tomohiko Uyematsu},
year=2005
}