Copyright © 2016 by Modern Scientific Press Company, Florida, USA International Journal of Information Science and System, 2016, 5(1): 1-7 International Journal of Information Science and System Journal homepage: www.ModernScientificPress.com/Journals/IJINFOSCI.aspx ISSN: 2168-5754 Florida, USA Article New Generalized Measure of Entropy of Order α and type β and Its Coding Theorems Ashiq Hussain Bhat* and M. A. K. Baig P.G. Department of Statistics, University of Kashmir, Srinagar-190006 * Author to whom correspondence should be addressed: E-Mail: ashiqhb14@gmail.com; baigmak@gmail.com Article history: Received 27 January 2016, Received in revised form 23 April 2016, Accepted 30 April 2016, Published 5 May 2016. Abstract: In this paper we present a new generalized measure of entropy of order and type . This measure is not only new but some known measures are the particular cases of our proposed measure. We also obtained the bounds for this measure. Keywords: Shannon’s entropy, Code-word length, Kraft inequality, Coding theorem, Holder’s inequality and Optimal code length. 1. Introduction The growth of telecommunication in the early twentieth century led several researchers to study the information control of signals , the seminal work of Shannon [1], based on papers by Nyquists [2,3] and Hartley [4] rationalized these early efforts into a coherent mathematical theory of communication and initiated the area of research now known as information theory. It is a new branch of probability and statistics with extensive potential application to communication system. The term information theory does not possess a unique definition. Broadly speaking, information theory deals with the study of problems concerning any system. This includes information processing, information storage and decision making. In a narrow sense, information theory studies all theoretical problems connected with the transmission of information over communication channels. This includes the study