O kvaternionech. [I.]
One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
One considers representation of cubic polynomials in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the...
Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.