Recursive constructions of image-polynomials over image Original Research Article

This paper presents procedures for constructing irreducible polynomials over image with linearly independent roots (or normal polynomials or N-polynomials). For a suitably chosen initial N-polynomial image of degree n, polynomials image of degrees image are constructed by iteratively applying the transformation image, and their roots are shown to form a normal basis of image over image. In addition, the sequences are shown to be trace compatible, i.e., the trace map image from image onto image maps the roots of image onto those of image.