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Eucidean lattices from numbers fields and coding theroy

Grant number: 13/13400-7
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): August 01, 2013
Effective date (End): July 31, 2014
Field of knowledge:Engineering - Electrical Engineering - Telecommunications
Principal Investigator:Edson Donizete de Carvalho
Grantee:Celso Toshio Takahashi
Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

In this work, we obtain Euclidean 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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