Quasi-perfect Geometrically Uniform Codes Derived From Graphs Over Gaussian Integer Rings

In this paper we present a generalization of the perfect codes derived from the quotient rings of Gaussian integers. We call this class of codes quasi-perfect, which in addition to preserving the property of being geometrically uniform codes they are able to correct more error patterns than the perfect codes. © 2010 IEEE.11581162Forney, G.D., Geometrically uniform codes (1991) IEEE Trans. on Inform. Theory, 37 (5), pp. 1241-1260. , SeptemberGolomb, S.W., Welch, L.R., Perfect codes in the lee metric and the packing of the polyominoes (1970) SIAM J. Applied Mathematics, 18 (2), pp. 302-317Costa, S.I., Muniz, M., Agustini, E., Palazzo, R., Graphs, tessellations, and perfect codes on flat tori (2004) IEEE Trans. on Inform. Theory, 50 (10), pp. 2363-2377. , OctoberMartínez, C., Beivide, R., Gabidulin, E., On the perfect t-dominating set problem in circulant graphs and codes over Gaussian integers (2005) Proc. IEEE Intl. Symp. Information Theory, pp. 254-258. , Adelaide, Australia, SeptemberMartínez, C., Beivide, R., Gabidulin, E., Perfect codes from metrics induced by circulant graphs (2007) IEEE Trans. on Inform. Theory, 53 (9), pp. 3042-3052. , SeptemberMartínez, C., Beivide, R., Gabidulin, E., Perfect codes from cayley graphs over lipschitz integers (2009) IEEE Trans. on Inform. Theory, 55 (8), pp. 3552-3562. , AugustSamuel, P., (1967) Algebraic Theory of Numbers, , Herman, ParisStewart, I., Tall, D., (1987) Algebraic Number Theory, , New York: Chapman-HallHungerford, T.W., (1974) Algebra, , New York: Springer Verla