CryptoDB
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
Authors: | |
---|---|
Download: | |
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 }