# N-Dimensional Binary Vector Spaces

Formalized Mathematics (2013)

• Volume: 21, Issue: 2, page 75-81
• ISSN: 1426-2630

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## Abstract

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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.

## How to cite

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Kenichi Arai, and Hiroyuki Okazaki. "N-Dimensional Binary Vector Spaces." Formalized Mathematics 21.2 (2013): 75-81. <http://eudml.org/doc/267159>.

@article{KenichiArai2013,
abstract = {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.},
author = {Kenichi Arai, Hiroyuki Okazaki},
journal = {Formalized Mathematics},
keywords = {formalization of binary vector space; binary vector space},
language = {eng},
number = {2},
pages = {75-81},
title = {N-Dimensional Binary Vector Spaces},
url = {http://eudml.org/doc/267159},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Kenichi Arai
AU - Hiroyuki Okazaki
TI - N-Dimensional Binary Vector Spaces
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 2
SP - 75
EP - 81
AB - 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.
LA - eng
KW - formalization of binary vector space; binary vector space
UR - http://eudml.org/doc/267159
ER -

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