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I am wondering whether you could still call a code something that, if transmitting, only transmits one symbol. Or does the formal definition of code require 2 or more symbols? (and would the answer change if that symbol can have different intensities, so perhaps having 2 or more intensities makes this a code?) thanks!

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The definition in the theory of codes does not require the alphabet to have two or more symbols, see for example the textbook by Berstel and Perrin. Over a one-letter alphabet the only codes are exactly the one-word sets. So mathematically this is not as interesting as bigger alphabets.

If your symbol can have different intensities, the most obvious way of formally modelling is to use different symbols for the different intensities. With this you would end up with a code over a bigger alphabet.

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  • $\begingroup$ thanks Peter. do you have a specific part of that book in mind? $\endgroup$ – magnolia1 Jul 22 '17 at 13:04
  • $\begingroup$ The definition of code is on page 37, @matteoeoeo. $\endgroup$ – Peter Leupold Jul 22 '17 at 13:34

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