Let be a Cyclic Code of length (where is odd)
Let be a field extension of
A defining set of is a set with the property:
Note that necessarily for nonempty .
Also need not be unique
We say a Cyclic Code is defined by if:
We usually work with the Splitting Field of
(which can be shown to be where )
This wasn’t done in lectures like this
See Cyclic Code with Defining Set