Algebro geometric methods in coding theory

Abstract

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.