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Quasi-cyclic subcodes of cyclic codes
Jean-Claude Belfiore, Cem Güneri, Buket Özkaya · 2016-03-16 · via cs.IT updates on arXiv.org

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

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