<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

N-Dimensional Binary Vector Spaces

This research was presented during the 2013 International Conference on Foundations of
Computer Science FCS’13 in Las Vegas, USA

Formalized Mathematics

{"article-title":"N-Dimensional Binary Vector Spaces"}

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...

N-Dimensional Binary Vector Spaces

Published Online: Jun 01, 2013

Page range: 75 - 81

DOI: https://doi.org/10.2478/forma-2013-0008

Keywords
formalization of binary vector space

This content is open access.

N-Dimensional Binary Vector Spaces

Published Online: Jun 01, 2013

Page range: 75 - 81

DOI: https://doi.org/10.2478/forma-2013-0008

Keywordsformalization of binary vector space

This content is open access.

Keywords
formalization of binary vector space