Algebraic Geometry Codes

This chapter introduces algebraic geometry (AG) codes. Algebraic geometry codes have good properties and some families of these codes have been shown to be asymptotically good. Concepts and notions relevant to AG codes are discussed with particular emphasis laid on the construction of AG codes. A generalised construction of AG codes is introduced and improvements to the tables of best-known codes are presented. This construction utilises the notion of places of higher degree of a curve as well as a new concatenation concept.