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2013 | 21 | 2 | 75-81

Tytuł artykułu

N-Dimensional Binary Vector Spaces

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
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.

Słowa kluczowe

Wydawca

Rocznik

Tom

21

Numer

2

Strony

75-81

Opis fizyczny

Daty

wydano
2013-06-01

Twórcy

autor
  • Tokyo University of Science Chiba, Japan
  • This research was presented during the 2013 International Conference on Foundations of
    Computer Science FCS’13 in Las Vegas, USA
  • Shinshu University Nagano, Japan

Bibliografia

  • [1] Jesse Alama. The vector space of subsets of a set based on symmetric difference. FormalizedMathematics, 16(1):1-5, 2008. doi:10.2478/v10037-008-0001-7.[Crossref]
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  • [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [6] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [7] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.
  • [8] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [9] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [12] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [13] X. Lai. Higher order derivatives and differential cryptoanalysis. Communications andCryptography, pages 227-233, 1994.
  • [14] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
  • [15] J.C. Moreira and P.G. Farrell. Essentials of Error-Control Coding. John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, 2006.
  • [16] Hiroyuki Okazaki and Yasunari Shidama. Formalization of the data encryption standard. Formalized Mathematics, 20(2):125-146, 2012. doi:10.2478/v10037-012-0016-y.[Crossref]
  • [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  • [18] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [20] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. FormalizedMathematics, 1(5):865-870, 1990.
  • [21] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1 (5):877-882, 1990.
  • [22] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
  • [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [24] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.
  • [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [27] Mariusz Zynel. The Steinitz theorem and the dimension of a vector space. FormalizedMathematics, 5(3):423-428, 1996.

Typ dokumentu

Bibliografia

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