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Published January 1, 2017 | Version v1
Journal article Open

QUASI-CYCLIC SUBCODES OF CYCLIC CODES

Creators

  • 1. Telecom ParisTech, Dept Comelec, 46 Rue Barrault, F-75634 Paris 13, France
  • 2. Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey

Description

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.

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