Primal-dual distance bounds of linear codes with application to cryptography
| dc.creator | Matsumoto, Ryutaroh | |
| dc.creator | Kurosawa, Kaoru | |
| dc.creator | Itoh, Toshiya | |
| dc.creator | Konno, Toshimitsu | |
| dc.creator | Uyematsu, Tomohiko | |
| dc.date | 2005-06-24 | |
| dc.date | 2006-06-12 | |
| dc.date.accessioned | 2026-07-07T08:15:30Z | |
| dc.date.available | 2026-07-07T08:15:30Z | |
| dc.description | 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. | |
| dc.description | 6 pages, using IEEEtran.cls. To appear in IEEE Trans. Inform. Theory, Sept. 2006. Two authors were added in the revised version | |
| dc.identifier | https://arxiv.org/abs/cs/0506087 | |
| dc.identifier | http://arxiv.org/abs/cs/0506087 | |
| dc.identifier | IEEE Trans. Inform. Theory, vol. 52, no. 9, pp. 4251-4256, Sept. 2006 | |
| dc.identifier | doi:10.1109/TIT.2006.880050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133468 | |
| dc.subject | Information Theory | |
| dc.subject | Cryptography and Security | |
| dc.title | Primal-dual distance bounds of linear codes with application to cryptography | |
| dc.type | text |