ON CODES CONSTRUCTED BY AN ALGEBRAIC CURVES OVER A FINITE FIELD
森田, 洋平MORITA, Yohei
562015-03-24 , 法政大学大学院理工学・工学研究科
The coding theory plays an important role in improving the reliability in information and communication. In particular, the error correcting code is applied to the _eld such as acoustic equipments and satellite communications. In the beginning of 1980's, V.D.Goppa, a mathematician, discovererd the algebraic geometry code. This code is the error correcting code based on algebraic geometry. It is possible to generate algebraic geometry code by using algebraic curves over a _nite _eld. We can estimate the information length and the minimum distance of these codes. However, there are many codes that are not constructed concretely. In this paper, we construct some concrete algebraic geometry codes by using an algebraic curve over a finite field.