Abstract
For any integer ρ ≥ 1 and for any prime power q, the explicit construction of an infinite family of completely transitive (and completely regular) q-ary codes with minimum distance d = 3 and with covering radius ρ is given.
This work has been partially supported by the Spanish MEC and the European FEDER Grants MTM2006-03250 and TSI2006-14005-C02-01 and also by the Russian fund of fundamental researches (the number of project 06 - 01 - 00226).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Borges, J., Rifa, J., Zinoviev, V.A.: On non-antipodal binary completely regular codes. Discrete Mathematics 308(16), 3508–3525 (2008)
Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer, Berlin (1989)
Cohen, G., Honkala, I., Litsyn, S., Lobstein, A.: Covering Codes. Elsevier, Amsterdam (1997)
Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips Research Reports Supplements 10 (1973)
Giudici, M., Praeger, C.E.: Completely Transitive Codes in Hamming Graphs. Europ. J. Combinatorics 20, 647–662 (1999)
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, New York (1977)
Neumaier, A.: Completely regular codes. Discrete Maths. 106/107, 335–360 (1992)
Rifa, J., Zinoviev, V.A.: On new completely regular q-ary codes. Problems of Information Transmission 43(2) (2007)
Rifa, J., Zinoviev, V.A.: On new completely regular codes from perfect codes. In: Proceedings of the Tenth Intern. Workshop on Algebraic and Combinatorial Coding Theory (ACCT-X), Zvenigorod, Russia, September 03-09 (2006)
Solé, P.: Completely Regular Codes and Completely Transitive Codes. Discrete Maths. 81, 193–201 (1990)
Semakov, N.V., Zinoviev, V.A., Zaitsev, G.V.: Class of maximal equidistant codes. Problems of Information Transmission 5(2), 84–87 (1969)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rifà, J., Zinoviev, V. (2008). On the Kronecker Product Construction of Completely Transitive q-Ary Codes. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-87448-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87447-8
Online ISBN: 978-3-540-87448-5
eBook Packages: Computer ScienceComputer Science (R0)