REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU

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dc.contributor.authorFuta, Yuichipl
dc.contributor.authorOkazaki, Hiroyukipl
dc.contributor.authorShidama, Yasunaripl
dc.date.accessioned2016-12-06T02:00:00Zpl
dc.date.accessioned2016-12-12T10:36:07Z-
dc.date.available2016-12-06T02:00:00Zpl
dc.date.available2016-12-12T10:36:07Z-
dc.date.issued2015pl
dc.identifier.citationFormalized Mathematics, Volume 23, Issue 1, Pages 29–49pl
dc.identifier.issn1426-2630pl
dc.identifier.issn1898-9934pl
dc.identifier.urihttp://hdl.handle.net/11320/4836-
dc.description.abstractIn this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [22] and coding theory [14]. Some theorems in this article are described by translating theorems in [24], [26] and [19] into theorems of ℤ-module.pl
dc.language.isoenpl
dc.publisherDe Gruyter Openpl
dc.subjectmatrix of Z-modulepl
dc.subjectmatrix of linear transformationpl
dc.subjectbilinear formpl
dc.titleMatrix of ℤ-modulepl
dc.typeArticlepl
dc.identifier.doi10.2478/forma-2015-0003pl
dc.description.AffiliationYuichi Futa - Japan Advanced Institute of Science and Technology, Ishikawa, Japanpl
dc.description.AffiliationHiroyuki Okazaki - Shinshu University, Nagano, Japanpl
dc.description.AffiliationYasunari Shidama - Shinshu University, Nagano, Japanpl
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Występuje w kolekcji(ach):Formalized Mathematics, 2015, Volume 23, Issue 1

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