Abstract
This work is twofold. First, the largest minimum distance of a ternary cyclic codes of parameters \({[n, \frac{n}{2}]}\), is determined for n even, not a multiple of 3, by using the Chen algorithm, for n = 26, 34, 38, 46, 50, 58, 62, 68, 70, 74. Next, seven new classes of isodual ternary cyclic codes are introduced for n singly even, not a multiple of 3.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cary Huffman, W., Pless, V.: Fundamentals of Error Correcting Codes. Cambridge University Press, Cambridge (2003)
Dougherty S.T., Gulliver T.A., Harada M.: Optimal ternary formally self-dual codes. Discrete Math. 196, 117–135 (1999)
Grassl, M.: Bounds on the minimum distance of linear codes (Electronic table; online). http://www.codetables.de.win/math/dw/voorlincood.html
MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)
Rains, E.M., Sloane, N.J.A.: Self-dual codes. In: Pless, V.S., Huffman, W.C. (eds.) Handbook of Coding Theory. Elsevier, Amsterdam (1998)
Voloch J.F.: Computing the minimal distance of cyclic codes. Comp. Appl. Math. 24, 393–398 (2005)
Acknowledgments
The authors thanks the referees for helpful suggestions that greatly improved the presentation of the material. They are very grateful to H. Aissaoui (Telecom ParisTech) for the optimization of the research algorithm of the minimum distance of a cyclic codes C [26, 13]3.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S.K. Jain.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Mihoubi, C., Solé, P. Optimal and isodual ternary cyclic codes of rate 1/2. Bull. Math. Sci. 2, 343–357 (2012). https://doi.org/10.1007/s13373-012-0027-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13373-012-0027-6