Key points are not available for this paper at this time.
In this paper we take a deeper look at the self conjugate reciprocal (SCR) polynomials, which towards the end of the paper aid the construction of new classes of permutation trinomials and quadrinomials over Fₐ^₂. The paper focuses on the conditions required for a certain class of degree 2 and degree 3 SCR polynomials to have no roots in ₐ+₁ (the set of (q+1) -th roots of unity), which helps in the determination of polynomials that permute Fₐ^₂. In the due course we also look upon some higher degree SCR polynomials which can be reduced down to a degree 2 SCR polynomial over both odd and even ordered fields. We furthur look upon the SCR polynomials of type ax^q+1+bx^q+bx+a^q taking both the cases under consideration where a Fₐ and aₐ^₂ₐ.
Sharma et al. (Mon,) studied this question.