TY - BOOK AU - Costa,Sueli I.R. AU - Oggier,Frédérique AU - Campello,Antonio AU - Belfiore,Jean-Claude AU - Viterbo,Emanuele ED - SpringerLink (Online service) TI - Lattices Applied to Coding for Reliable and Secure Communications T2 - SpringerBriefs in Mathematics, SN - 9783319678825 AV - QA639.5-640.7 U1 - 516.1 23 PY - 2017/// CY - Cham PB - Springer International Publishing, Imprint: Springer KW - Convex geometry  KW - Discrete geometry KW - Coding theory KW - Information theory KW - Data encryption (Computer science) KW - Convex and Discrete Geometry KW - Coding and Information Theory KW - Cryptology N1 - Introduction -- Lattices and Applications -- Lattices from Codes -- Ideal Lattices -- Lattices and Spherical Codes -- Lattice and Index Coding; Available to subscribing member institutions only. Доступно лише організаціям членам підписки N2 - 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 UR - https://doi.org/10.1007/978-3-319-67882-5 ER -