Good spherical codes must have large minimum squared distance. An important quota in the theory of spherical codes is the maximum number of points M(n, ρ) displayed on the sphere Sn-1, having a minimum squared distance ρ. The aim of this work is to study this problem restricted to the class of group codes. We establish a tighter bound for the number of points of a commutative group code in odd dimension, extending the bounds of [6]. © 2006 IEEE. 367369Ericson, T., Zinoviev, V., Codes on Euclidian Spheres (2001) North-Holland Mahtematical Libray, , Elsevier Science Pub CoVaishampayan, V., Costa, S.I.R., Curves on a Sphere, Shift-Map Dynamics, and Error Control for Continuos Alphabet Sources (2003) IEEE Transaction on Information Theory, 49 (7). , JulyCosta, S.I.R., Muniz, M., Agustini, E., Palazzo, R., Graphs, Tessellations, and Perfect Codes on Flat Tori (2004) IEEE Transaction on Information Theory, 50 (10). , OctoberIngermasson, I., Commutative group codes for the Gaussian Channel (1973) IEEE Transaction on Information Theory, IT-19, pp. 215-219. , MarGantmacher, F.R., (1959) The theory of matrices, 1. , Chelsea, New YorkSiqueira, R., Costa, S.I.R., Minimum Distance Upper Bounds for Commutative Group Codes (2006) Proceedings of IEEE Information Theory Workshop (ITW, , Uruguay, March 13-17Slepian, D., Group codes for the Gaussian Channel (1968) The Bell System Technical Journal, 4 (7), pp. 575-602. , AprilSloane, N.J.A., Conway, J.H., Sphere Packings, Lattices and Groups (1991) Springer-Verlag , 3 edtSloane, N.J.A., Nebe, G., Table of Densest Packings Presently Known, , http://www.research.att.com/njas/lattices/density.html, published electronically at