On Metric Dimension of Nonbinary Hamming Spaces
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For q-ary Hamming spaces we address the problem of the minimum number of points such that any point of the space is uniquely determined by its (Hamming) distances to them. It is conjectured that for a fixed q and growing dimension n of the Hamming space this number asymptotically behaves as 2n/ log q n. We prove this conjecture for q = 3 and q = 4; for q = 2 its validity has been known for half a century.
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- 1.Harary, F. and Meter, R.A., On the Metric Dimension of a Graph, Ars Combin., 1976, vol. 2, pp. 191–195.Google Scholar
- 2.Slater, P., Leaves on Trees, Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, Feb. 17–20, 1975), Hoffman, F., Mullin, R.C., Levow, R.B., Roselle, D., Stanton, R.G., and Thomas, R.S.D., Eds., Congr. Numer., vol. XIV, Winnipeg: Utilitas Math., 1975, pp. 549–599.Google Scholar
- 8.Kabatianski, G., Lebedev, V., and Thorpe, J., The Mastermind Game and the Rigidity of the Hamming Space, in Proc. 2000 IEEE Int. Sympos. on Information Theory (ISIT’2000), Sorrento, Italy, June 25–30, 2000, p.375.Google Scholar
- 11.Martirosian, S.S. and Khachatrian, G.G., Construction of Signature Codes and the Coin Weighing Problem, Probl. Peredachi Inf., 1989, vol. 25, no. 4, pp. 96–97 [Probl. Inf. Trans. (Engl. Transl.), 1989, vol. 25, no. 4, pp. 334–335].Google Scholar