The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional binary vector spaces are very important in proving the security of cryptographic systems [13]. In this article we define the n-dimensional binary vector space Vn. Moreover, we formalize some facts about the n-dimensional binary vector space Vn.
@article{bwmeta1.element.doi-10_2478_forma-2013-0008,
author = {Kenichi Arai and Hiroyuki Okazaki},
title = {N-Dimensional Binary Vector Spaces},
journal = {Formalized Mathematics},
volume = {21},
year = {2013},
pages = {75-81},
zbl = {1298.15005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0008}
}
Kenichi Arai; Hiroyuki Okazaki. N-Dimensional Binary Vector Spaces. Formalized Mathematics, Tome 21 (2013) pp. 75-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0008/
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