Browsing by Subject "variety"

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    Algebro geometric methods in coding theory
    (1999) Özen, İbrahim
    In this work, we studied a class of codes that, as a subspace, satisfy a certain condition for (semi)stability. We obtained the Poincare polynomial of the nonsingular projective variety which is formed by the equivalence classes of such codes having coprime code length n and number of information symbols k. We gave a lower bound for the minimum distance parameter d of the semistable codes. We show that codes having transitive automorphism group or those corresponding to point configurations having irreducible automorphism group are (semi)stable. Also a mass formula for classes of stable codes with coprime n and k is obtained. For the asymptotic case, where n and k tend to infinity while their ratio ^ is seperated both from 0 and 1, we show that all codes are stable.
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    Free actions on CW-complexes and varieties of square zero matrices
    (2011) Şentürk, Berrin
    Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology over k. Carlsson showed that this conjecture implies the rank conjecture about free actions on product of spheres. In this paper, to understand the Carlsson’s conjecture about differential graded modules, we study the structure of the variety of upper triangular square zero matrices and the techniques which were investigated by Rothbach to determine its irreducible components . We hope these varieties could help prove Carlsson’s conjecture.