Lay summary
Coding theory has emerged out of the need for better communication and has rapidly developed as a mathematical theory in strong relationship with algebra, combinatorics and algebraic geometry. Nowadays error-correcting-codes are used in everyday practical applications such as digital-storage media, wire-line and wireless networks, and satellite and deep-space communication systems. Example of simple block codes are the international standard book numbers (ISBN), the ASCII code and various encoding schemes used to identify bank accounts.Network coding theory is concerned with the encoding and transmission of information where there may be many information sources and possibly many receivers. R. Koetter and F. Kschischang identified a fundamental mathematical question which lies at the heart of network coding. This formulation seeks the construction of good subsets of the finite Grassmann variety and it is the intended plan of the proposed research to use algebraic techniques to come up with new network codes which have better throughput and efficient decoding.