125 kHz RFID reader with Arduino
Yes, Chris Stratton is right. A toroidal inductor keeps flux within the core, reduces the external flux to near zero and have near zero ability to grasp/convert external flux/magnetic field into electrical signal. Apparently, the word 'toroidal' was used in loose sense referring to a circularly shaped coil.

In an real-life commercial product, a 125&nbsp;kHz coil typically has many turns on a very thin wire on an open-air core (no core).

An example profession factory made a 125&nbsp;kHz RFID with a GitHub Arduino library and photos of an antenna coil:


125 kHz RFID module - UART
Seeed-Studio/RFID_Library
125Khz RFID module - UART (wiki)


Also, see Building RFID Card Reader using PIC Microcontroller.

Note, for higher frequency RFID, not shown in above examples, coils have fewer turns than for 125&nbsp;kHz.