Paper 2005/194
Primal-Dual Distance Bounds of Linear Codes with Application to Cryptography
Ryutaroh Matsumoto, Kaoru Kurosawa, Toshiya Itoh, Toshimitsu Konno, and 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.
Note: We added a table for the shortest input length of Boolean functions of EPC(l) of order k by the Kurosawa-Satoh construction in the revised version. Two authors were added. To appear in IEEE Trans. Inform. Theory, Sept. 2006.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- boolean functionlinear code
- Contact author(s)
- ryutaroh @ it ss titech ac jp
- History
- 2006-06-12: revised
- 2005-06-24: received
- See all versions
- Short URL
- https://ia.cr/2005/194
- License
-
CC BY
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} }