A new subclass of cyclic Goppa codes

We propose a subclass of cyclic Goppa codes given by separable self-reciprocal Goppa polynomials of degree two. We prove that this subclass contains all reversible cyclic codes of length $n$, $n\mid(q^m\pm1)$, with a generator polynomial $g(x)$, $g(\alpha^{\pm i})=0$, $i=0,1$, $\alpha^n=1$, $\alpha\in GF(q^{2m})$.