DOI: 10.1007/s10955-006-9142-7. On the High Density Behavior of Hamming Codes with Fixed Minimum Distance

On the High Density Behavior of Hamming Codes with Fixed Minimum Distance

10.1007/s10955-006-9142-7

Crossref journal-article

Springer Science and Business Media LLC

Journal of Statistical Physics (297)

Bibliography

Parisi, G., & Zamponi, F. (2006). On the High Density Behavior of Hamming Codes with Fixed Minimum Distance. Journal of Statistical Physics, 123(6), 1145â1167.

Authors 2

Giorgio Parisi (first)
Francesco Zamponi (additional)

References 17 Referenced 6

E. N. Gilbert, A comparison of signalling alphabets, Bell Syst. Tech. Jnl. 31: 504–522 (1952); (10.1002/j.1538-7305.1952.tb01393.x)
R. R. Varshamov, Estimate of the number of signals in error correcting codes, Dokl. Akad. Nauk SSSR 117: 739–741 (1957).
P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl. 10: 1–97 (1973). / Philips Res. Rep. Suppl. by P. Delsarte (1973)
R. J. McEliece, E. R. Rodemich, H. Rumsey and L. R. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans.Inform.Theory 23: 157–166 (1977). (10.1109/TIT.1977.1055688) / IEEE Trans.Inform.Theory by R. J. McEliece (1977)
A. Procacci and B. Scoppola, Statistical mechanics approach to coding theory, J. Stat. Phys. 96: 907–912 (1999). (10.1023/A:1004666811087)
A. Barg and D. B. Jaffe, Numerical results on the asymptotic rate of binary codes, in Codes and Association Schemes (A. Barg and S. Litsyn, Eds.), Amer. Math. Soc. Providence, 2001 (10.1090/dimacs/056/02)
A. Samorodnitsky, On the Optimum of Delsarte’s Linear Program, J. Com. Theo., Series A 96: 261–287 (2001). (10.1006/jcta.2001.3176) / J. Com. Theo., Series A by A. Samorodnitsky (2001)
H. L. Frisch and J. K. Percus, High dimensionality as an organizing device for classical fluids, Phys. Rev. E 60: 2942–2948 (1999). (10.1103/PhysRevE.60.2942) / Phys. Rev. E by H. L. Frisch (1999)
G. Parisi and F. Slanina, A toy model for the mean-field theory of hard-sphere liquids, Phys. Rev. E 62: 6554–6559 (2000). (10.1103/PhysRevE.62.6554) / Phys. Rev. E by G. Parisi (2000)
G. Parisi and F. Zamponi, Amorphous packings of hard spheres in large space dimension, J. Stat. Mech. (2006) P03017. (10.1088/1742-5468/2006/03/P03017)
O. U. Uche, F. H. Stillinger and S. Torquato, On the realizability of pair correlation functions, Physica A 360: 21–36 (2006); (10.1016/j.physa.2005.03.058)
S. Torquato and F. H. Stillinger, New provisional lower bounds on the optimal density of sphere packings, J. Expe. Mat., in press.
J.-P. Hansen and I. R. MacDonald, Theory of simple liquids (Academic Press, London, 1986). / Theory of simple liquids by J.-P. Hansen (1986)
Eric W. Weisstein, Krawtchouk Polynomial, From MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com/KrawtchoukPolynomial.html
A. Lenard, States of classical statistical mechanics of infinitely many particles: I, II, Arch. Rational. Mech. Anal. 59: 219–239, 241–256 (1975). (10.1007/BF00251601)
T. Kuna, J. L. Lebowitz and E. Speer, On the realizability of point processes with specified one and two particle densities, Math.Frosch.Oberwolfach 43: (2004), Large Scale Stochastic Dynamics, ed. C. Landim, S. Olla, H. Spohn, O. Costin and J. L. Lebowitz, On the construction of particle distributions with specified single and pair densities, J. Phys. Chem. 108: 19614 (2004).
G. Parisi and F. Zamponi, The ideal glass transition of hard spheres, J. Chem. Phys. 123: 144501 (2005). (10.1063/1.2041507) / J. Chem. Phys. by G. Parisi (2005)

Dates

Type	When
Created	19 years, 1 month ago (July 11, 2006, 10:40 a.m.)
Deposited	6 years, 2 months ago (June 2, 2019, 1:42 a.m.)
Indexed	2 years ago (Aug. 18, 2023, 3:12 p.m.)
Issued	19 years, 2 months ago (June 1, 2006)
Published	19 years, 2 months ago (June 1, 2006)
Published Online	19 years, 1 month ago (July 12, 2006)
Published Print	19 years, 2 months ago (June 1, 2006)

Funders 0

None

BibTeX

@article{Parisi_2006, title={On the High Density Behavior of Hamming Codes with Fixed Minimum Distance}, volume={123}, ISSN={1572-9613}, url={http://dx.doi.org/10.1007/s10955-006-9142-7}, DOI={10.1007/s10955-006-9142-7}, number={6}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Parisi, Giorgio and Zamponi, Francesco}, year={2006}, month=jun, pages={1145–1167} }

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