Eucidean lattices from numbers fields and coding theroy

• Grant number: 13/13400-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2013
• End date: 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.