Abstract
As a common generalization of constant weight binary codes and permutation codes, constant composition codes (CCCs) have attracted recent interest due to their numerous applications. In this paper, a class of new CCCs are constructed using design-theoretic techniques. The obtained codes are optimal in the sense of their sizes. This result is established, for the most part, by means of a result on generalized doubly resolvable packings which is of combinatorial interest in its own right.
Similar content being viewed by others
References
Beth T., Jungnickel D., Lenz H. (1999) Design Theory. Cambridge Univ. Press, Cambridge, UK
Chee Y.M., Ling A.C.H., Ling S., Shen H. (2007) The PBD-closure of constant composition codes. IEEE Trans. Inform. Theory 53(8): 2685–2692
Chu W., Colbourn C.J., Dukes P. (2006) On constant composition codes. Discrete Appl. Math. 154: 912–929
Colbourn C.J., Dinitz J.H. (2007) The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton, FL
Csiszar I., Kornner J. (1981) Information Theory: Coding Theorems for Discrete Memoryless Channels. Academic Press, New York
Ding C., Yin J. (2005) Combinatorial constructions of optimal constant composition codes. IEEE Trans. Inform. Theory 51: 3671–3674
Ding C., Yin J. (2006) A construction of constant composition codes. Des. Codes Cryptogr. 40: 157–165
Furino S., Miao Y., Yin J. (1996) Frames and Resolvable Designs. CRC Press, Boca Raton, FL
Hall Jr. M.: Combinatorial Theory, 2nd edn. John Wiley & Sons (1986).
Luo Y., Fu F.W., HanVinck A. J., Chen W. (2003) On constant composition codes over Z q . IEEE Trans. Inform. Theory 49: 3010–3016
Stanton R.G., Mullin R.C. (1968) Construction of room squares. Ann. Math. Statist. 39: 1540–1548
Svanström M.: Ternary codes with weight constraints. Ph.D. dissertation, Linköpings University, Sweden (1999).
Wilson R.M. (1972) Cyclotomy and difference families in elementary abelian groups. J. Number Theory 4: 17–47
Yan J., Yin J.: Constructions of optimal GDRP(n,λ;v)′s of type λ1μm-1. Discrete Appl. Math. (in press).
Yin J., Yan J., Wang C. (2008) Generalized balanced tournament designs of block size 4. Des. Codes Cryptogr. 46: 211–230
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by C. J. Colbourn.
Rights and permissions
About this article
Cite this article
Yan, J., Yin, J. A class of optimal constant composition codes from GDRPs. Des. Codes Cryptogr. 50, 61–76 (2009). https://doi.org/10.1007/s10623-008-9214-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-008-9214-6