The impedance for a half wave antenna is high at both ends. Around 3 kΩ.
For a 50Ω coax feed line a 50x (2,5kΩ) to 70x (3,5kΩ) impedance transformer is needed.
A winding ratio of 4 (for example) transforms the voltage a factor 4 up and the current a factor 4 down (equal power). This means the impedance transformation is the square of the turn / winding ratio. So in this example a impedance transformation of 16, giving a 800Ω output impedance.
Primary and secondary windings are bifilar wound (and loosely twisted).