Amplitude Shift Keying coding
Regarding the harmonics: ASK has an infinite number of them. The ASK signal can be thought of as a square wave multiplied by a sinusoid. In frequency, this corresponds to the spectrum of the square wave shifted to the frequency of the sinusoid. Since the spectrum of the square wave is infinite, the spectrum of the ASK signal is infinite too.

In practice, the ASK signal is filtered to force it to fit in a specific bandwidth. This has the effect of distorting the signal, but if done carefully the distortion is not severe. In any case, ASK is only used in applications where bandwidth is not a constraint.

I recommend the following procedure to understand how to generate an ASK signal. First you need to map "bits" to "voltages" (also called "amplitudes"). Bits are abstract quantities that do not have physical substance, while voltages are physical. In ASK you typically map a bit 0 to 0 volts, and a bit 1 to $A$ volts. Now you can generate a sequence of voltages that corresponds to your bits:

$$ \text{bits}=\lbrace 0,1,1,0,1,1,0,1 \rbrace$$

$$ \text{amplitudes} = \lbrace 0, A, A, 0, A, A, 0, A \rbrace $$

Now you need to define a pulse $p(t)$ of duration $T_b$:

$$ p(t) = \begin{cases}1,\quad0\leq t\leq T_b,\\0,\quad\text{otherwise}\end{cases} $$

(You will eventually want to control the energy of the pulse by changing its amplitude).

The next step is to define the "baseband" ASK (that is, with no carrier) signal:

$$ s_{BB}(t) = \sum_{k=0}^7 a_k p(t-kTb) $$ where $a_k$ is the $k$-th amplitude (starting from 0), and $p(t-kT_b)$ is the pulse shifted $kT_b$ seconds "to the right". Take a moment to study this equation and you'll see that it is a train of pulses of amplitude 0 for a bit 0 and amplitude A for a bit 1.

Now you're ready to create the ASK signal, which is:

$$ s(t) = s_{BB}(t)\sin(2\pi f_c t) $$

To transmit more bits per pulse, all you need to is to increase the range of values of the amplitudes.

I know that this is different from the way most undergrad textbooks teach this subject, but I still think it makes more sense to think about it this way.