사영직선 위의 MDS 대수기하 부호

Abstract

The algebraic geometry code was introduced in 1981 by V.D. Goppa. Goppa discovered the relationship between algebraic geometry and error correcting code and studied the composition of error correcting codes using the algebraic functional field. Algebraic geometry code have been important in code theory for a long time. The algebraic geometry code on algebraic straight line is called the rational algebraic geometry code, and the Reed-Solomon code is seen as the algebraic geometry code on an affine line. In this thesis, we look at the algebraic geometry code on a projective line and show that this code is the MDS code. Then, find the general matrix and dual code of this code and obtain the parity check matrix of the original code. It is shown that the dual code of this code is also MDS code.