I. Introduction
We consider the process of transmitting data over a channel where the data being sent can be thought as a stream of symbols from a finite alphabet . The data stream consists of consecutive messages, each message being a sequence of consecutive symbols. The synchronization problem that arises at the receiving end is the task to partition correctly the data stream into messages of length , as opposed to conceiving incorrectly a sequence of symbols being the concatenation of the end of one message with the beginning of another message as a single message. One way to resolve the synchronization problem is by requiring that the collection of admissible messages, or code , has the property that no single message coincides with a concatenation c_{i}(x, y)=x_{i+1}\ldots x_{n}y_{1}\ldots y_{i} of two (not necessarily different) messages . This property can be expressed formally in terms of the comma-free index of the code , defined as \rho=\min d(z, c_{i}(x, y)), where the minimum is taken over all and all , and is the Hamming distance. If the comma-free index is positive, it is possible to distinguish a codeword from a concatenation of two codewords even in case that up to errors have occurred in the given codeword [2].