Modeling hexagonal constellations with Eisenstein-Jacobi graphs
Problems of Information Transmission
Perfect codes from Cayley graphs over Lipschitz integers
IEEE Transactions on Information Theory
Quotients of Gaussian graphs and their application to perfect codes
Journal of Symbolic Computation
Frobenius circulant graphs of valency six, Eisenstein-Jacobi networks, and hexagonal meshes
European Journal of Combinatorics
Dense bipartite circulants and their routing via rectangular twisted torus
Discrete Applied Mathematics
| Hi-index | 754.90 |
An algebraic methodology for defining new metrics over two-dimensional signal spaces is presented in this work. We have mainly considered quadrature amplitude modulation (QAM) constellations which have previously been modeled by quotient rings of Gaussian integers. The metric over these constellations, based on the distance concept in circulant graphs, is one of the main contributions of this work. A detailed analysis of some degree-four circulant graphs has allowed us to detail the weight distribution for these signal spaces. A new family of perfect codes over Gaussian integers will be defined and characterized by providing a solution to the perfect t-dominating set problem over the circulant graphs presented. Finally, we will show how this new metric can be extended to other signal sets by considering hexagonal constellations and circulant graphs of degree six.