Abstract
We construct a class of perfect codes for an additive channel. The class contains classical Hamming codes.
Similar content being viewed by others
References
Deza, M.E., On Correction of an Arbitrary Noise and on the Worst Noise, in Probl. Peredaci Inf., issue 16, Moscow: Nauka, 1964, pp. 26–31.
Goppa, V.D., Correction of Arbitrary Noise by Irreducible Codes, Probl. Peredachi Inf., 1974, vol. 10, no. 3, pp. 118–119 [Probl. Inf. Trans. (Engl. Transl.), 1974, vol. 10, no. 3, pp. 277–278].
Krichevskii, R.E., Szhatie i poisk informatsii, Moscow: Radio i Svyaz’, 1989. Translated under the title Universal Compression and Retrieval, Dordrecht: Kluwer, 1994.
Leont’ev, V.K. and Movsisyan, G.L., On an Additive Communication Channel, Dokl. Nats. Akad. Nauk Armen., 2004, vol. 104, no. 1, pp. 23–28.
Leont’ev, V.K., Movsisyan, G.L., and Margaryan, Zh.G., Perfect Codes in Additive Channels, Dokl. Ross. Akad. Nauk, 2006, vol. 411, no. 3, pp. 306–308 [Dokl. Math. (Engl. Transl.), 2006, vol. 74, no. 3, pp. 831–833].
Leont’ev, V.K. and Movsisyan, G.L., Algebraic Communication Channels, in Proc. 1st Int. Algebra and Geometry Conf., Yerevan, Armenia, 2007, pp. 16–20.
Zinoviev, V.A. and Leont’ev, V.K., On Non-existence of Perfect Codes over Galois Fields, Probl. Upravlen. Teor. Inform., 1973, vol. 2, no. 2, pp. 123–132 [Probl. Control Inf. Theory (Engl. Transl.), 1973, vol. 2, no. 2, pp. 16–24].
Tietäväinen, A., On the Nonexistence of Perfect Codes over Finite Fields, SIAM J. Appl. Math., 1973, vol. 24, no. 1, pp. 88–96.
Solov’eva, F.I., On Perfect Codes and Related Topics, Com2MaC Lect. Note Ser., vol. 13, Pohang, Korea: Pohang Univ. of Science and Technology (POSTECH), 2004.
Krotov, D.S. and Avgustinovich, S.V., On the Number of 1-Perfect Binary Codes: A Lower Bound, IEEE Trans. Inform. Theory, 2008, vol. 54, no. 4, pp. 1760–1765.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.K. Leont’ev, G.L. Movsisyan, J.G. Margaryan, 2008, published in Problemy Peredachi Informatsii, 2008, Vol. 44, No. 4, pp. 12–19.
Supported in part by the Russian Foundation for Basic Research, project no. 08-01-00414a.
Rights and permissions
About this article
Cite this article
Leont’ev, V.K., Movsisyan, G.L. & Margaryan, J.G. On perfect codes for an additive channel. Probl Inf Transm 44, 295–302 (2008). https://doi.org/10.1134/S0032946008040029
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0032946008040029