http://www.cnr.it/ontology/cnr/individuo/prodotto/ID686
On the high density behavior of Hamming codes with fixed minimum distance (Articolo in rivista)
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- On the high density behavior of Hamming codes with fixed minimum distance (Articolo in rivista) (literal)
- Anno
- 2006-01-01T00:00:00+01:00 (literal)
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- Parisi, G; Zamponi, F (literal)
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- ISI Web of Science (WOS) (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy; Univ Roma La Sapienza, Ist Nazl Fis Nucl, INFM, CRS SMC, I-00185 Rome, Italy; Ecole Normale Super, Phys Theor Lab, F-75231 Paris, France (literal)
- Titolo
- On the high density behavior of Hamming codes with fixed minimum distance (literal)
- Abstract
- We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> infinity, d ->infinity , d/n = delta. The problem is relevant for coding theory, and the best available bounds state that the maximum density of the system falls in the interval 1 <= rho V (d) <= exp (n kappa(delta)), being kappa(delta) > 0 and V-d the volume of a sphere of radius d. We find a solution of the equations describing the liquid up to an exponentially large value of (rho) over tilde = rho V-d , but we show that this solution gives a negative entropy for the liquid phase for (rho) over tilde greater than or similar to n. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. (literal)
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