I thought that a coil of wire might be good as an antenna. If this is valid would using said antenna improve reception and transmittance if used? Would an antenna of this kind be stronger with more turns in its winding?
I thought that a coil of wire might be good as an antenna.
There are a lot of antennas that could be described as "a coil of wire", and some of them are pretty good, but there's a lot more to antenna design than just randomly coiling wires.
If this is valid would using said antenna improve reception and transmittance if used?
As opposed to no antenna at all -- maybe. If the size of the coil is closer to the wavelength of your signal than the antenna terminals on your radio, then probably. As opposed to an optimal antenna -- no, pretty much by the definition of "optimal".
Would an antenna of this kind be stronger with more turns in its winding?
Only if it didn't have enough turns to begin with. If it already had enough, or too many, then no.
Short answer, probably not, no. Radio waves (RF) is a highly complex field of study, separate from traditional electronics; it would take a book to explain even the basics of RF.
In essence, the antenna must be tuned to the frequency of interest. "Tuning" is both a mechanical and electrical property. "Tuning" is only good for a narrow band of frequencies centered around the target frequency (unless multiple antennas are used, but that imposes other issues.) The biggest effect on tuning is the length of the antenna - shorter antennas pickup higher frequencies. At higher frequencies, all sorts of physical and electrical properties change, which greatly compound their design.
So if interested in a specific frequency, it is far easier to just buy an antenna ready-made for that frequency.
If you want to research further, here is a RF Basics document from Maxim to get you started.
There are at several kinds of antennas which could be described as "coils of wire", with very different principles.
small loop antennas are actual coils (often with ferrite rods), though they are woven differently from power inductors or actuator coils, as self-capacitance must be reduced. These are tuned by a variable capacitor which is used to complete the LC-circuit with a given resonant frequency. Unlike most other antennas, they are coupled to the magnetic component of the EM-field, and are only good for reception.
full loop antennas look like coils, but operate as groups of folded dipoles. They are tuned to a particular frequency by the perimeter of the loop which must match one wavelength.
helix antennas also look like coils or springs, although they are nothing more than quarter-whip monopoles folded into a helical shape to reduce the size. They are (roughly) tuned a frequency by their unfolded length, which must be between one quarter and one half of a wavelength.