Constructive recognition of classical groups in even characteristic

Let G=〈X〉⩽GL(d,F)G=〈X〉⩽GL(d,F) be a classical group in its natural representation defined over a finite field FF of even characteristic. We present Las Vegas algorithms to construct standard generators for G which permit us to write an element of G as a straight-line program in X, and to construct an involution as a straight-line program in X  . If |F|>4|F|>4, then the algorithms run in time polynomial in the size of the input, subject to the existence of a discrete logarithm oracle for FF.