Abstract
In this paper, the basic function field of an asymptotically optimal tower of function fields by Garcia and Stichtenoth is studied, where bases of one-point linear systems can be explicitly constructed. A representation of finite GF(q 2 )-rational points on the associated plane curve is derived and exploited to develop a real-time hardware architecture for the calculation of syndromes needed in the decoding of AG codes built on this curve. © 2010 IEEE.