REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: `http://hdl.handle.net/11320/3675`
Pole DCWartośćJęzyk
dc.contributor.authorArai, Kenichi-
dc.contributor.authorOkazaki, Hiroyuki-
dc.date.accessioned2015-12-09T20:39:33Z-
dc.date.available2015-12-09T20:39:33Z-
dc.date.issued2013-
dc.identifier.citationFormalized Mathematics, Volume 21, Issue 2, 2013, Pages 75-81-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3675-
dc.descriptionThis research was presented during the 2013 International Conference on Foundations of Computer Science FCS’13 in Las Vegas, USA-
dc.description.abstractThe 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.-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.subjectformalization of binary vector space-
dc.titleN-Dimensional Binary Vector Spaces-
dc.typeArticle-
dc.identifier.doi10.2478/forma-2013-0008-
dc.description.AffiliationArai Kenichi - Tokyo University of Science Chiba, Japan-
dc.description.AffiliationOkazaki Hiroyuki - Shinshu University Nagano, Japan-
dc.description.referencesJesse Alama. The vector space of subsets of a set based on symmetric difference. Formalized Mathematics, 16(1):1-5, 2008. doi:10.2478/v10037-008-0001-7.-
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
dc.description.referencesCzesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.-
dc.description.referencesCzesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.-
dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.-
dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
dc.description.referencesEugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.-
dc.description.referencesX. Lai. Higher order derivatives and differential cryptoanalysis. Communications and Cryptography, pages 227-233, 1994.-
dc.description.referencesRobert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.-
dc.description.referencesJ.C. Moreira and P.G. Farrell. Essentials of Error-Control Coding. John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, 2006.-
dc.description.referencesHiroyuki Okazaki and Yasunari Shidama. Formalization of the data encryption standard. Formalized Mathematics, 20(2):125-146, 2012. doi:10.2478/v10037-012-0016-y.-
dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.-
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.-
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
dc.description.referencesWojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990.-
dc.description.referencesWojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1 (5):877-882, 1990.-
dc.description.referencesWojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.-
dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
dc.description.referencesMariusz Zynel. The Steinitz theorem and the dimension of a vector space. Formalized Mathematics, 5(3):423-428, 1996.-
Występuje w kolekcji(ach):Formalized Mathematics, 2013, Volume 21, Issue 2

Pliki w tej pozycji:
Plik Opis RozmiarFormat