Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes. (2016)

• Record Type: Journal Article
• Authors: Tamo, Itzhak; Barg, Alexander; Goparaju, Sreechakra; Calderbank, Robert
• Is Part Of: International journal of information and coding theory. Volume 3:Number 4(2016)
• Page Start: 345
• Page End: 364
• Publication Date: 2016
• Subjects: locally recoverable codes -- cyclic LRC codes -- irreducible cyclic codes -- subfield subcodes -- binary LRC codes -- upper bounds -- distance-optimal cyclic codes -- dual distance; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.