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Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes
by Itzhak Tamo; Alexander Barg; Sreechakra Goparaju; Robert Calderbank
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 4, 2016
Abstract: We consider linear cyclic codes with the locality property or locally recoverable codes (LRC codes). A family of LRC codes that generalises the classical construction of Reed-Solomon codes was constructed in a recent paper by Tamo and Barg (IEEE Transactions on Information Theory, No. 8, 2014). In this paper, we focus on distance-optimal cyclic codes that arise from this construction. We give a characterisation 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. The locality parameter of a cyclic code is related to the dual distance of this code, and we phrase our results in terms of upper bounds on the dual distance.
Online publication date: Wed, 21-Sep-2016
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