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Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes. (English) Zbl 1410.94121

Summary: 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 I. Tamo and A. Barg [IEEE Trans. Inf. Theory 60, No. 8, 4661–4676 (2014; Zbl 1360.94385)]. 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.

MSC:

94B15 Cyclic codes
94B05 Linear codes (general theory)

Citations:

Zbl 1360.94385
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