Packing and Covering Radii of Linear Error-Block Codes
Authors: Rabiˆı DARITI, El Mamoun SOUIDI
Abstract:
Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.
Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088270
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2184References:
[1] K. Feng, L. Xu and F.J. Hickernell: Linear error-block codes. Finite Fields
Appl. 12, 638–652 (2006).
[2] S. Ling, F. O¨ zbudak: Constructions and bounds on linear error-block
codes. Designs, Codes and Cryptography. 45, 297–316 (2007).
[3] M.M.S. Alves, L. Panek, M. Firer: Error-block codes and poset metrics.
Advances in Mathematics of Communications. Vol. 2, No. 1,95–111
(2008).
[4] R. Dariti, E. M. Souidi, New Families of Perfect Linear Error-Block
Codes, International Journal of Information and Coding Theory. Accepted
for publication (2012).
[5] R. Dariti, E. M. Souidi,Cyclicity and Decoding of Linear Error-Block
Codes, Journal of Theoretical and Applied Information Technology, 25,
No. 1 (2011).
[6] R. Dariti, E.M. Souidi, Improving Code-Based Steganography with Linear
Error-Block Codes. Digital Information Processing and Communications,
Communications in Computer and Information Science, International
Conference, ICDIPC 2011, Ostrava, Czech Republic, July 7-9, 2011,
Proceedings, Part II, Springer Berlin Heidelberg. 189, 310–321 (2011).
[7] G. Cohen, I. Honkala, S. Litsyn, and A. Lobstein: Covering Codes.
Amsterdam, The Netherlands: North-Holland, 1997.
[8] H.F. Mattson: An Upper Bound on Covering Radius. Combinatorial
Mathematics, Proceedings of the International Colloquium on Graph
Theory and Combinatorics, North-Holland, 75, 453 – 458 (1983).
[9] W.C. Huffman, V. Pless: Fundamentals of Error-Correcting Codes. Cambridge
University Press (2003).