Quasi-cyclic subcodes of cyclic codes
Belfiore, Jean-Claude and Güneri, Cem and Özkaya, Buket (2017) Quasi-cyclic subcodes of cyclic codes. SIAM Journal On Discrete Mathematics, 31 (2). pp. 1454-1475. ISSN 0895-4801 (Print) 1095-7146 (Online)
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Official URL: http://dx.doi.org/10.1137/16M1065604
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 elds. 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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