The Mattson – Solomon Transformation and Modified Cyclonomials

The study of the weight spectrum of minimal cyclic codes, as started in refs. 2 and 3, is continued. It appeared that the properties (especially their number) of zeros of a special type of the cyclonomials, and also of the so-called modified cyclonomials, are essential for the structure and computation of this weight spectrum. To understand the behavior of these zeros we study in this report the irreducible polynomials over GF q( ) which are contained in the polynomial mq x x − , in particular those which have trace value zero. In the context of this study we investigate the notion of dual space of ( ) m GF q considered as a vector space and also its various normal bases and the duals of those bases. In the final section we presentthese notions extensively for the case 4 GF(3 ).