Abstract
Binary codes that can be obtained from designs associated with circulant graphs G(n, S) are studied. The parameters of the codes and the information sets are obtained. PD-sets for full-error correction are found for certain values of n.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Assmus E.F. Jr., Key J.D.: Designs and Their Codes. Cambridge Tracts in Mathematics, vol. 103. Cambridge University Press, Cambridge (1992) (Second printing with corrections, 1993)
Frucht R.: On the groups of repeated graphs. Bull. Am. Math. Soc. 55, 418–520 (1949)
Harary F.: The automorphism group of the hypercube. J. Univers. Comput. Sci. 6, 136–138 (2000)
Huffman W.C.: Codes and groups. In: Pless V.S., Huffman W.C. (eds.) Handbook of Coding Theory, vol. 2, Part 2, Chap. 17, pp. 1345–1440. Elsevier, Amsterdam.
Key J.D., Seneviratne P.: Permutation decoding of binary codes from lattice graphs. Discrete Math. 308, 2862–2867 (2008)
Key J.D., Moori J., Rodrigues B.G.: Permutation decoding for the binary codes from triangular graphs. Eur. J. Comb. 25, 113–123 (2004)
MacWilliams F.J.: Permutation decoding of systematic codes. Bell Syst. Tech. J. 43, 485–505 (1964)
MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1998)
Whitney H.: Congruent graphs and the connectivity of graphs. Am. J. Math. 54, 154–168 (1932)
Author information
Authors and Affiliations
Corresponding author
Additional information
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding Theory and Applications”.
Rights and permissions
About this article
Cite this article
Seneviratne, P. Codes associated with circulant graphs and permutation decoding. Des. Codes Cryptogr. 70, 27–33 (2014). https://doi.org/10.1007/s10623-012-9637-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-012-9637-y