Let len : A −→ N be the length function on the free monoid of all strings over a given non-empty finite set A. Let con : A −→ A be the concatenation map which to every string of strings associates their concatenation. A uniquely decipherable code is a finite set C ⊆ A such that con is injective on the submonoid C of A. This submonoid is then isomorphic to the submonoid C = con[C] of A freely ge...

In present communication, we have developed the suitable constraints for the given the mean codeword length and the measures of entropy. This development has proved that Renyi’s entropy gives the minimum value of the log of the harmonic mean and the log of power mean. We have also developed an important relation between best 1:1 code and the uniquely decipherable code by using different measure...

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite

The theory of uniquely decipherable (UD) codes has been widely developed in connection with automata theory, combinatorics on words, formal languages, and monoid theory. Recently, the concepts ofmultiset decipherable (MSD) and set decipherable (SD) codes were developed to handle some special problems in the transmission of information. Unique decipherability is a vital requirement in a wide ran...

The objective of the present communication is to develop new genuine exponentiated mean codeword lengths and to study deeply the problem of correspondence between well known measures of entropy and mean codeword lengths. With the help of some standard measures of entropy, we have illustrated such a correspondence. In literature, we usually come across many inequalities which are frequently used...

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical codi...

‎Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: ‎s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map‎. ‎We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points‎. ‎Moreover‎, ‎we show that if $h(sigma_P)=0$‎, ‎then $Sigma_...

∈∆N ), (1.1) where the convention 0log(0)= 0 is adapted, (see Shannon [19]). Throughout this paper, ∑ will stand for ∑N i=1 unless otherwise stated and logarithms are taken to the baseD (D > 1). Let a finite set of N input symbols X = {x1, x2, . . . ,xN } be encoded using alphabet of D symbols, then it has been shown by Feinstien [6] that there is a uniquely decipherable code with lengths n1,n2...

we extend some results of Lempel and Restive on multiset decipherable codes to set decipherable codes. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Codes, Unique decipherability, Multiset decipherability, Dominoes, Set decipherability.