Let C be the cyclic code defined by a primitive nth root of unity.
This is the start of a question I have been given, but I don't understand how this is a valid way to define a cyclic code. The way I learnt to define them is by giving a generating function for the code.
Now clearly given a primitive nth root of unity it is possible to find a minimal polynomial which it satisfies. Is that what the question means? That the generating function is just this?