Study od Coding-Theory

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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.