English

Cyclic LRC Codes and their Subfield Subcodes

Information Theory 2015-02-06 v1 math.IT

Abstract

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Transactions on Information Theory, no. 8, 2014; arXiv:1311.3284). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.

Keywords

Cite

@article{arxiv.1502.01414,
  title  = {Cyclic LRC Codes and their Subfield Subcodes},
  author = {Itzhak Tamo and Alexander Barg and Sreechakra Goparaju and Robert Calderbank},
  journal= {arXiv preprint arXiv:1502.01414},
  year   = {2015}
}

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R2 v1 2026-06-22T08:22:37.141Z