We completely characterize possible indices of quasi-cyclic subcodes in acyclic code for a very broad class of cyclic codes. We present enumerationresults for quasi-cyclic subcodes of a fixed index and show that the problem ofenumeration is equivalent to enumeration of certain vector subspaces in finitefields. In particular, we present enumeration results for quasi-cyclic subcodesof the simplex code and duals of certain BCH codes. Our results are based onthe trace representation of cyclic codes.
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