CONSTRUCTION OF POLYNOMIALS IRREDUCIBLE OVER A FINITE FIELD WITH LINEARLY INDEPENDENT ROOTS
Igor Semaev · Mathematics of the USSR-Sbornik · 1989
For any the author gives a method of constructing a matrix — the multiplication table for a certain normal basis of the finite field over , where is a power of a prime . The characteristic polynomial of is an irreducible polynomial of degree with coefficients in , whose roots are linearly independent over . In order to construct the matrix , and thus an irreducible polynomial with linearly independent roots, one needs to perform no more than additions and multiplications in (where is the greatest prime divisor of ). Bibliography: 3 titles.