Circulant Graphs And Spherical Codes

Circulant graphs are homogeneous graphs with special properties which have been used to build interconnection networks for parallel computing. The association of circulant graphs to a spherical codes in dimension 2 k is presented here via the construction of an isomorphic graph supported by a lattice in ℝk. © 2006 SBrT.4245Adam, A., Research problem 2-10 (1967) J. Combinatorial Theory, 2, p. 393Biglieri, E., Elia, M., Cyclic-Group Codes for the Gaussian Channel (1976) IEEE Trans. Inform. Theory, Correspondence, pp. 624-629F. Boesch, R. Tindell, Circulant and Their Connectivities, J. of Graph Theory, 8 (1984) 487-499Costa, S.I.R., Muniz, M., Agustini, E., Palazzo, R., Graphs, Tessellations, and Perfect Codes on Flat Tori (2004) IEEE Trans. Inform. Theory, 50 (10), pp. 2363-2378Costa, S.I.R., Strapasson, J.E., Muniz, M., Carlos, T.B., Siqueira, R.M., Circulant Graphs Viewed as Graphs on Flat Tori SubmittedElpas, B., Turner, J., Graphs with circulant adjacency matrices (1970) J. Combin. Theory, 9, pp. 229-240Liskovets, V., Pöschel, R., Counting circulant graphs of prime-power order by decomposing into orbit enumeration problems (2000) Discrete Mathematics, 214, pp. 173-191Martínez, C., Beivide, R., Gutierrez, J., Gabidulin, E., On the Perfect t-Dominanting Set Problem in Circulant Graphs and Codes over Gaussian Integers (2005) Proceedings ISIT - IEEE International Symposium on Information Theory, pp. 1-5Slepian, D., Group codes for the Gaussian Channel (1968) The Bell System Technical Journal, 47, pp. 575-602Siqueira, R., Costa, S.I.R., Minimum Distance Upper Bounds for Commutative Group Codes (2006) Proceedings of IEEE Information Theory Workshop (ITW, , Uruguay, March 13-1