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Lattices Applied to Coding for Reliable and Secure Communications [electronic resource] / by Sueli I.R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo.

By: Costa, Sueli I.R [author.].
Contributor(s): Oggier, Frédérique [author.] | Campello, Antonio [author.] | Belfiore, Jean-Claude [author.] | Viterbo, Emanuele [author.] | SpringerLink (Online service).
Material type: TextTextSeries: SpringerBriefs in Mathematics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: VI, 120 p. 43 illus., 33 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319678825.Subject(s): Discrete groups | Coding theory | Data encryption (Computer scienc | Convex and Discrete Geometry | Coding and Information Theory | Data EncryptionAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 516.1 Online resources: Click here to access online
Contents:
Introduction -- Lattices and Applications -- Lattices from Codes -- Ideal Lattices -- Lattices and Spherical Codes -- Lattice and Index Coding.
In: Springer eBooksSummary: This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.
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Introduction -- Lattices and Applications -- Lattices from Codes -- Ideal Lattices -- Lattices and Spherical Codes -- Lattice and Index Coding.

This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.

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