Explicit equations for maximal curves as subcovers of the BM curve

Abstract Let r ≥ 3 be an odd integer and F q 2 r the finite field with q 2 r elements. A second generalisation of the Giulietti-Korchmaros maximal curve over F q 6 was presented in 2018 by Beelen and Montanucci, the so-called BM curve. This curve is maximal over F q 2 r and isomorphic to the Giulietti-Korchmaros curve for r = 3 . In this paper, benefiting from suitable representations of the automorphism group of the BM curve, we construct explicit equations for families of maximal algebraic curves as Galois subcovers of the BM curve, we also provide the genus and the Galois group associated to the subcover.