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Abstract
We establish a new upper bound for binary arithmetic codes, which is asymptotically better than previously known bounds. We also discuss possible “candidates” such as Plotkin and Elias bounds for arithmetic codes over an arbitrary alphabet.
The second author is greatly indebted to the first one for inviting him for a 6-week stay at the Institute for Problems of Information Transmission.
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References
W.W. Peterson, E.J. Weldon, Jr.: Error-correcting codes. Cambridge: MIT Press 1972
J.L. Massey, O.N. Garcia: Error-correcting codes in computer arithmetics. In: Advances in Information Systems Science 4, New York-London: Plenum Press 1972, Ch. 5
G.A. Kabatianski: Bounds on the number of code words in binary arithmetic codes. Problems of Information Transmission 12-4, 277–283 (1976)
R.J. McEliece, E.R. Rodemich, H.C. Rumsey, Jr., L.R. Welch: New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities. IEEE IT-23, 157–166 (1977)
E.R. Berlekamp (ed.): Key papers in the development of coding theory. New-York IEEE Press 1974
L.A. Bassalygo: New upper bounds for codes correcting errors. Problems of Information Transmission 6-4, 41–45 (1965), in Russian
P. Solé: A Lloyd theorem in weakly metric association schemes. Europ. J. Combinatorics 10, 189–196 (1989)
Ph. Delsarte: An algebraic approach to the association schemes of coding theory. Philips Research Reports Suppl. 10, 1973
V.I. Levenshtein: Designs as maximum codes in polynomial metric spaces. Acta Applicandae Mathematicae 25, 1–I, 1992
I.M. Boyarinov, G.A. Kabatianski: Arithmetic (n,A)-codes over an arbitrary base. Sov. Phys. Dokl. 20-4, 247–249 (1975)
W.E. Clark, J. J. Liang: On modular weight and cyclic nonadjacent forms for arithmetic codes. IEEE-IT 20, 767–770 (1974)
S. Ernvall: On bounds for nonbinary arithmetic codes. Ars Combinatoria 29-B, 85–89 (1990)
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Institute for Problems of Information Transmission, Ermolovoy 19, GSP-4, Moscow, Russia
Gregory Kabatianski
Dpt INF, Centre National de la Recherche Scientifique Télécom Paris, 46 rue Barrault, 75634, Paris Cedex 13, France
Antoine Lobstein
- Gregory Kabatianski
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- Antoine Lobstein
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© 1994 Springer-Verlag Berlin Heidelberg
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Kabatianski, G., Lobstein, A. (1994). On Plotkin-Elias type bounds for binary arithmetic codes. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_27
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