Abstract
In this thesis, we analyze the algebraic structure of rational points in a Hermitian curve. By combinging Horner's rule with this special sturcture, an architecture of syndrome calculator in the decoding of a Hermitian code is proposed. At the same time, this work also leads to a rational point generator of a Hermitian curve, which can be applied to the search of error locators in the decoding of Hermitian codes. Finally, a design example of a Hermitian code based on the Hermitian curve x5+y4+y=0 is illustrated for VLSI implementation.