Quasi-cyclic subcodes of cyclic codes
Information Theory
2016-03-17 v1 math.IT
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 BCH codes. Our results are based on the trace representation of cyclic codes.
Keywords
Cite
@article{arxiv.1603.05063,
title = {Quasi-cyclic subcodes of cyclic codes},
author = {Jean-Claude Belfiore and Cem Güneri and Buket Özkaya},
journal= {arXiv preprint arXiv:1603.05063},
year = {2016}
}