Algebras of Primitive Idempotent Generators and Zeros of Cyclonomials

In [7] the algebra generated by generating polynomials of primitive constacyclic codes , , was studied. It appeared that there is a kind of duality between the set of these polynomials and the set of so-called constacyclonomials. This duality shows some resemblance with the duality between irreducible characters and classes of conjugated elements of finite groups. In the present report this phenomenon of duality is studied more closely for the special case of primitive cyclic codes i.e. for . Among other results it is shown that the well-known Mattson-Solomon transformation fits perfectly in this picture of duality, since it transforms primitive idempotents to cyclonomials and vice versa. The relationship between the weight of a codeword of a cyclic code and the zeros of its M.S. transform can be seen as another aspect of this duality. Because of this reason the zeros of cyclonomials form the subject of the final section.