There will be a broad range of values for the ferrite core and number of turns that would suit reception of a 60kHz transmission. Firstly, because it is only 60kHz, virtually any ferrite core material would do because at that frequency, the losses in most ferrite materials are going to be negligible.
Secondly, the ferrite core and winding will resonate with a tuning capacitor to form what is known as a tuned-circuit. The general idea here is that the tiny magnetic field from the 60kHz signal received is converted into a voltage (by the coil) and amplified many times by the action of a coil and capacitor. This gives you two things: -
- A bigger signal to deal with (better of course)
- Rejection of other signals that are out of the 60kHz band
In other words, signal is improved and noise is reduced. Here's what wiki says about this: -
AM broadcast radios (and some other receivers used at low frequencies)
typically use small loop antennas; a variable capacitor connected
across the loop forms a tuned circuit that tunes the radio's
Because resonant frequency is dependent on inductance and capacitance there is a broad sway of coil configurations that are suitably tuned by different capacitances achieving the same (or nearly the same) performance but, in general, you would try and make the coil's inductance is high as possible to achieve higher Q. Q is how much the circuit resonates and therefore for a low bandwidth signal you re better with more rather than fewer turns on the ferrite core.
After the ferrite core there is a strong possibility that no further LC tuning is done and that the AM signal is amplified by simple IC's or transistors. The signal will then feed an envelope detector. This will produce a signal that "follows" the amplitude of the 60kHz carrier frequency - the data is encoded as changes of carrier amplitude and so the envelope detector produces an output voltage that is the data. This can be fed into a comparator circuit and then on to a microprocessor for digital decoding of the signal.