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)
PDF
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
Creative Commons Attribution
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}
}
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