Lattice of ℤ-module

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2017-05-16T09:30:38Z	-
dc.date.available	2017-05-16T09:30:38Z	-
dc.date.issued	2016	-
dc.identifier.citation	Formalized Mathematics, Volume 24, Issue 1, pp. 49-68	pl
dc.identifier.issn	1426-2630	pl
dc.identifier.issn	1898-9934	pl
dc.identifier.uri	http://hdl.handle.net/11320/5490	-
dc.description.abstract	In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	ℤ-lattice	-
dc.subject	Gram matrix	-
dc.subject	integral ℤ-lattice	-
dc.subject	positive definite ℤ-lattice	-
dc.title	Lattice of ℤ-module	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2016-0005	-
dc.description.Affiliation	Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University Nagano, Japan	-
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