On the perfect t-dominating set problem in circulant graphs and codes over gaussian integers

The basis for designing error-correcting codes for two dimensional signal sets is considered in this paper. Both, algebraic and graph-theoretical approaches are employed in this research for establishing the fundamentals of these codes. We give a solution to the t-dominating set problem in a subfamily of degree four circulant graphs which directly provides perfect codes over the Gaussian integers. In order to show the applicability of our results, simple examples for designing different coding schemes are also presented