Study od Coding-Theory

1. 我们对g属的光滑投影代数曲线C进行分类，使特殊线性系统W^2_(C)的变化具有g - 7维数。我们证明了W^2_(C)的维数g - 7 <大于等于>当且仅当C是三角形曲线、二属曲线的双重覆盖、g^3_非常充裕的曲线或g^2_.2的曲线。我们将g属的光滑投影代数曲线C分类为通常生成的线束度<大于等于> 2g - 3。并且证明了当g < >或等于> 6k3时，通常会生成每一个极充裕的、次为2g + 1 - k <或等于> 2g - 5且h^1(L) = h <或等于> max（2, (k - 4)/3）的线束L。证明了d <大于等于> g - (k - 2) [(h+3)/] - h+ 1时W^1_(C)的不可约性，其中C是一条g属曲线，它允许一个奇素数次k映射到一般曲线C的h属> 0上。此外，还证明了在曲线C上覆盖X的一般k片上W^1_(X)具有期望维数的分量的存在性。

1. We classify smooth projective algebraic curves C of genus g such that the variety of special linear systems W^2_(C) has dimension g - 7. We prove that W^2_(C) has dimension g - 7 <greater than or equal> 0 if and only if C is either a trigonal curve, a double cover of a curve of genus two, a curve with very ample g^3_ or a curve with g^2_.2. We classify smooth projective algebraic curves C of genus g with normally gen-erated line bundle of degree <greater than or equal> 2g - 3. And we prove that every very ample line bundle L of degree 2g + 1 - k <less than or equal> 2g - 5 with h^1(L) = h <greater than or equal> max(2, (k - 4)/3) is normally generated, if g <greater than or equal> 6k3. Irreducibility of W^1_(C) for d <greater than or equal> g - (k - 2) [(h+3)/] - h + 1, where C is a curve of genus g which admits an odd prime degree k map onto a general curve C of genus h > 0 is proved. Also, the existence of a component of W^1_(X) with expected dimension on a general k-sheeted covering X over a curve C is shown.