International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 315686, 10 pages
http://dx.doi.org/10.1155/2012/315686
Research Article

Some Coding Theorems for Nonadditive Generalized Mean-Value Entropies

Satish Kumar,1 Gurdas Ram,2 and Vishal Gupta3

1Department of Mathematics, Geeta Institute of Management and Technology, Kurukshetra, Kanipla 136131, India
2Department of Applied Sciences, Maharishi Markandeshwar University, Solan 173229, India
3Department of Mathematics, Maharishi Markandeshwar University, Mullana 133203, India

Received 8 July 2011; Accepted 7 December 2011

Academic Editor: Andrei Volodin

Copyright © 2012 Satish Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give an optimality characterization of nonadditive generalized mean-value entropies from suitable nonadditive and generalized mean-value properties of the measure of average length. The results obtained cover many results obtained by other authors as particular cases, as well as the ordinary length due to Shannon 1948. The main instrument is the 𝑙 ( 𝑛 𝑖 ) function of the word lengths in obtaining the average length of the code.