Perfect graph codes over two dimensional lattices
Carmen Martínez, Cristóbal Camarero, Ramón Beivide · 2010
In this paper we consider perfect codes over two dimensional QAM-type constellations of any cardinal. Such constellations are going to be modeled by L-graphs, which are the two-dimensional family of multidimensional circulants, defined. We show that Gaussian graphs, Lee graphs and the Kronecker product of two cycles are included in this family. Therefore, our method to obtain perfect codes over these lattice subsets is a generalization of the techniques for searching perfect two-dimensional Lee codes and perfect codes over the Kronecker products of two cycles. In addition, we introduce some previously unreported perfect codes.