Paper 2005/194 Original: eprint.iacr.org/2005/194 ↗
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2006-06-12: last updated
- 2005-06-24: published
- Short URL
- https://ia.cr/2005/194
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/194,
author = {Ryutaroh Matsumoto and Kaoru Kurosawa and Toshiya Itoh and Toshimitsu Konno and Tomohiko Uyematsu},
title = {Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/194},
year = {2005},
url = {https://eprint.iacr.org/2005/194}
}