Kodlama teorisinde cebirsel geometrik metotlar

ABSTRACT ALGEBRO GEOMETRIC METHODS IN CODING THEORY Ibrahim Özen M.S. in Mathematics Supervisor: Prof. Dr. Alexander A. Klyachko 1999 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 sym bols 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 au tomorphism 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. Keywords: Linear code, variety, moduli sapce, stability, point configu ration. m