Summary
A random sequential packing by Hamming distance is applied to study Golay code. The probability of getting Golay code is estimated by computer simulation. A histogram of number of packed points is given to show the existence of several remarkable clusters.
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References
Bernal, J. D. (1959) A geometrical approach to the structure of liquids,Nature,17, 141–147.
Golay, M. J. E. (1949) Notes on digital coding,Proc. I.R.E. (I.E.E.E.),37, 657.
Hamming, R. W. (1947).Self-Correcting Codes-Case 20878, Memorandum 1130-RWH-MFW, Bell Telephone Laboratories, July 27, 1947.
Higuti, I. (1960) A statistical study of random packing of unequal spheres,Ann. Inst. Statist. Math.,12, 257–271.
Itoh, Y. (1980) On the minimum of gaps generated by one-dimensional random packing,J. Appl. Prob.,17, 134–144.
Itoh, Y. (1985) Note on a restricted random cutting of a stick,Proc. Inst. Statist. Math.,33, 97–99. (In Japanese with English summary).
Itoh, Y. (1985) Abstract of research works in 1984 “random packing by Hamming distance”,Proc. Inst. Statist. Math.,33, 156–157. (In Japanese).
Itoh, Y. and Solomon, H. (1986). Random sequential coding by Hamming distance,J. Appl. Prob. (to appear).
Leech, J. (1964) Some sphere packings in Higher space,Canad. J. Math.,16, 657–682.
MacWilliams, E. J. and Sloane, N. J. A. (1977).The Theory of Error-Correcting Codes, I, II, North-Holland.
Peterson, W. W. (1961).Error-Correcting Codes, M.I.T. Press, Cambridge, Massachusetts.
Rényi, A. (1958) On a one-dimensional problem concerning random space filling,Publ. Math. Inst. Hung. Acad. Sci.,3, 109–127.
Shannon, C. E. (1948) A mathematical theory of communication,Bell System Tech. J.,27, 379–423, 623–656.
Sloane, N. J. A. (1984). The packing of spheres,Scientific American, January, 116–125.
Solomon, H. (1967) Random packing density,Proc. Fifth Berkeley Symp. Math. Stat. Prob.,3, 119–134, Univ. of California Press.
Tanemura, M. (1979) On random complete packing by discs,Ann. Inst. Statist. Math.,31, 351–365.
Thompson, T. M. (1983). From error-correcting codes through sphere packing to simple groups,The Mathematical Association of America.
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Itoh, Y. Golay code and random packing. Ann Inst Stat Math 38, 583–588 (1986). https://doi.org/10.1007/BF02482545
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DOI: https://doi.org/10.1007/BF02482545