Network algebraic codes and applications

Nowadays, it is an important issue to store or transmit information from one point to another without any loss or error. Therefore, some efficient coding algorithms have been used to reduce the error or loss. Primarily, information can be shared by computers and there must be a computer network. In these networks, information is shared by using some different coding algorithms.In the first part of this thesis, an introduction will be given about the definition and history of the network connection and its coding algorithm which is studied in this work. Then, some basic definitions and theorems which are related to networks, graph theory and network coding are explained. To understand how network coding is implemented, some explanations and examples are used. Especially, linear network codes and transformation matrices are introduced. It is specified under which conditions network coding processing and connections which is determined, is occured. In addition, there are also some basic definitions and theorems about error detection and correction in network connection coding algorithms.Consequently, there are some results and suggestions about network coding.Key words: Network, network coding, graph theory, lineer codes, error correction, error detection.