A family of binary (t, m,s)-nets of strength 5
Document Type
Article
Publication Date
11-2005
Department
Department of Mathematical Sciences
Abstract
(t,m,s)-Nets were defined by Niederreiter [Monatshefte fur Mathematik, Vol. 104 (1987) pp. 273-337], based on earlier work by Sobol' [Zh. Vychisl Mat. i mat. Fiz, Vol. 7 (1967) pp. 784-802], in the context of quasi-Monte Carlo methods of numerical integration. Formulated in combinatorial/coding theoretic terms a binary linear (m-k,m,s)2-net is a family of ks vectors in F 2m satisfying certain linear independence conditions (s is the length, m the dimension and k the strength: certain subsets of k vectors must be linearly independent). Helleseth et al. [5] recently constructed (2r-3,2r+2,2 r -1)2-nets for every r. In this paper, we give a direct and elementary construction for (2r-3,2r+2,2 r +1) 2-nets based on a family of binary linear codes of minimum distance 6.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Bierbrauer, J.,
&
Edel, Y.
(2005).
A family of binary (t, m,s)-nets of strength 5.
Designs, Codes, and Cryptography,
37(2), 211-214.
http://doi.org/10.1007/s10623-004-3986-0
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4870