Excuse me I am a complete beginner. If LF radio waves are sent with let’s say frequencies of 100 kHz, how can data be modulated to that signal considering the signal is so long? For example, how can let’s say a 40-bit code be transmitted on that LF radio wave over a short distance like 10 feet using modulation?
Any form of modulation requires a non-zero bandwidth. If I send only a simple sine wave with no modulation, the receiver can't get any information out of that signal because I didn't put any into it. Its like a pendulum continuing to swing at the same frequency and amplitude, so you can't tell anything else about it (it contains no other information). But if I start pushing on the pendulum at different times and with different forces, its amplitude will vary and also the frequency energy will not always be at exactly the free-swinging frequency. So any modulation will always produce energy at other frequencies. So someone else observing the pendulum can get information from it (specifically, the information about how I varied my pushing of the pendulum).
Now let's say I amplitude modulate a signal such that there are 10000 different amplitude levels, and each level means something different. If there is no noise in the system, and the receiver can measure those levels, then obviously I can send a lot of data. Even if its a 1Hz carrier, that's still 10000 different levels per second. However, in practice all signals have a bit of noise (undesirable energy) in them. The noise can come from a variety of sources. We've found that the theoretical maximum data rate that can be sent through a channel (assuming ideal modulation) depends on the maximum allowed power, maximum allowed frequency bandwidth, and the noise (see Shannon-Hartley theorem).
Also note that ideal modulation means that the entire allowed band is filled with otherwise unpredictable data (consider that any predictability in the data is not "new" information, and therefore wastes bandwidth). So for ideal modulation, this means you won't even see the carrier frequency any more than any other frequency.