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Title: Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes
Authors: Itzhak Tamo; Alexander Barg; Sreechakra Goparaju; Robert Calderbank
Department of EE-Systems, Tel Aviv University, Tel Aviv, Israel
Department of ECE and ISR, University of Maryland, College Park, MD 20742, USA; IITP, Russian Academy of Sciences, Moscow, Russia
CALIT2, University of California, San Diego, 9500 Gilman Drive #0436, La Jolla, CA 92093, USA
Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
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.
Keywords: locally recoverable codes; cyclic LRC codes; irreducible cyclic codes; subfield subcodes; binary LRC codes; upper bounds; distance-optimal cyclic codes; dual distance.
Int. J. of Information and Coding Theory, 2016 Vol.3, No.4, pp.345 - 364
Submission date: 23 Mar 2016
Date of acceptance: 17 Apr 2016
Available online: 21 Sep 2016