From binary codes to lattices and spherical codes / De codigos binarios a reticulados e codigos esfericos
AUTOR(ES)
Anderson Tiago da Silva
DATA DE PUBLICAÇÃO
2007
RESUMO
In this work it is presented through examples a connection between inary codes, lattices and spherical codes. A brief introduction to coding theory, properties and examples is included in the first chapter. In Chapter 2 lattices are approached with focus on the quotient of lattices, graphs on flat tori and connections with circulant graphs. An introduction to spherical codes and some of their bounds, as the Ranking bound, are described in Chapter 3. Finally in Chapter 4 the three topics above are connected. The construction of lattices from linear binary codes and the construction of spherical codes from the lattices which have orthogonal sub-lattices are presented. We analyze specifically the case of the three dimensional BCC lattice, which has the best packing density for this dimension, and show that a quotient of this lattice give rise to the best spherical code associate to the commutative group Z2 2 ×Z4. We also identify the lattice which is associate to the best commutative group code with 16 elements in em R6
ASSUNTO(S)
lattice theory sphere packings teoria dos reticulados empacotamento de esferas codigos de controle de erros (teoria da informação) error-correcting codes (information theory)
