The references mentioned in the other answer do not really pertain too much to the problem of minimax approximation; they are more concerned with the other functions in
FunctionApproximations` that deal with numerical differential equation solving; that is, the content that was once in the old
Indeed, a look at the contents of the old
NumericalMath`Approximations` package, where
GeneralMiniMaxApproximation once was, yields the following refs:
Carl-Erik Fröberg, Numerical Mathematics: Theory and Computer Applications, Benjamin/Cummings, 1985, pp. 250-266
A. Ralston & P. Rabinowitz, A First Course in Numerical Analysis (2nd. ed.), McGraw-Hill, New York, 1978
I do not possess a copy of the first ref, but I have a copy of the second one; the discussion of Remez's second algorithm is here. The papers in that book's bibliography are also to be pursued.