| Around 1980, Goppa discovered a beautiful construction of linear codes based on algebraic curves. In 1982, Tsmasman et al. proved there exist asymptotically good codes achieving the Tsfasman-Vladut-Zink bound, which beats the Gilbert-Varshamov bound. In recent years the Tsfasman-Vladut-Zink lower bound on the standard functionα_q(δ) was improved by several mathematicians.In this thesis, we study the construction problem of algebraic geometry codes from maximal curves. We give a condition for the existence of algebraic geometry codes with the prescribed parameters. We also study the generalized algebraic geometry codes introduced by Xing, Niederreiter and Lam. |
