Recursive construction of normal polynomials over finite fields

Abstract

Recently, Kim and Son [9] have obtained an infinite sequence of irreducible polynomials over the finite field F_q of characteristic p by using the transformation . Here, it is shown that one can also build this infinite sequence of irreducible polynomials over the field F_q of characteristic p by using a different transformation . Moreover, this transformation is helpful to establish the sequence of normal polynomials of degree np^r in F_q[x] by using an appropriate initial normal polynomial of degree n.

Subject Classification:

• 12E05
• 12E10
• 12E20

Keywords:

• Finite field
• Irreducible polynomial
• Normal polynomial
• Self -reciprocal polynomial