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Algebraic densest lattices

Grant number: 18/21829-7
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): February 01, 2019
Effective date (End): December 31, 2019
Field of knowledge:Engineering - Electrical Engineering - Telecommunications
Principal Investigator:Edson Donizete de Carvalho
Grantee:Bruna Neves Machado
Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

In this work, we obtain lattices from algebraic number fields. The interesting of this subject, as consequence the proof of source coding theorem. It was shown it possibility to obtain optimum block codes for noise channel (AWGN), when we obtain dense lattices in high dimension. However, we obtain maximum density of lattices, when we obtain minimum discriminant of number field.

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