Dimension Of Two-Point Codes On The Quotient Of Hermitian Curves

The construction and decoding of algebraic geometry codes are one of the hotspots in modern encoding theory. The parameters of codes on the curves over finite fields is always the important problem in algebraic geometry codes. In this paper, we summarize the foundations of Algebraic function fields, algebraic curves over finite fields and algebraic geometry codes, then we focus on the dimensions of codes on the quotient of the hermitian curves, by using the theory of weierstrass semigroup and the idea of Homma and Kim, and the main results as follows:1. we determine the dimensions of one-point codes on the quotient of the hermitian curves.2. we determine the dimensions of two-point codes on the quotient of the hermitian curves.