Abstract
Locally repairable codes (LRCs) are a class of codes which can recover from erasures by accessing a small number of erasure-free code symbols. The objective of this letter is to present a generic construction of q-ary cyclic LRCs via cyclotomic polynomials over the finite filed F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , where q is any prime power. Some properties of cyclotomic polynomials are employed to determine the dimension and minimum distance of the proposed LRCs. This idea was inspired by a recent construction by Kim and No where they used a special class of cyclotomic polynomials over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> to generate binary cyclic LRCs. Our construction extends the earlier one and yields new optimal or almost optimal cyclic LRCs with respect to certain bounds.
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