A deterministic construction for normal bases of abelian extensions

摘要

In this paper we give a deterministic construction for a Normal basis of Kf over K, where K' is an abelian extension of finite degree n over some commutative, infinite field K. No particular property for K is needed.We use polynomials already defined in 2, 5, chapter 5, In these papers the field K was finite. These polynomials were used in order to construct SDMC codes 5,chapter 6, to determine bivariate codes 2,3, or to obtain the best possible principal nilpotent codes 6, Our construction is deduced from new properties of these polynomials