QUASI-CYCLIC SUBCODES OF CYCLIC CODES

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Belfiore J., Guneri C., Ozkaya B.

SIAM JOURNAL ON DISCRETE MATHEMATICS, vol.31, no.2, pp.1454-1475, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1137/16m1065604
  • Journal Name: SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1454-1475
  • Keywords: cyclic code, quasi-cyclic code, subcode, index, enumeration, CURVES
  • Middle East Technical University Affiliated: No

Abstract

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.