Code construction on fiber products of Kummer covers

We show that Riemann-Roch spaces of divisors from fiber products of Kummer covers of the projective line, which are invariant with respect to the Galois group, decompose as a direct sum of Riemann-Roch spaces of divisors of the projective line. Consequently, one obtains explicit bases and good upper bounds for the minimum distance of the resulting Goppa codes. This correspondence is a generalization of the work of Xing.