QUASI-CYCLIC SUBCODES OF CYCLIC CODES

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Date

2017-01-01

Author

Belfiore, Jean-Claude
Guneri, Cem
Özkaya, Buket

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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 Bose-Chaudhuri-Hocquenqhem codes. Our results are based on the trace representation of cyclic codes.

Subject Keywords

cyclic code, quasi-cyclic code, subcode, index, enumeration, CURVES

URI

https://hdl.handle.net/11511/103975

Journal

SIAM JOURNAL ON DISCRETE MATHEMATICS

DOI

https://doi.org/10.1137/16m1065604

Collections

Graduate School of Applied Mathematics, Article

Citation Formats

J.-C. Belfiore, C. Guneri, and B. Özkaya, “QUASI-CYCLIC SUBCODES OF CYCLIC CODES,” SIAM JOURNAL ON DISCRETE MATHEMATICS, vol. 31, no. 2, pp. 1454–1475, 2017, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/103975.