Optimal Cyclic Locally Repairable Codes via Cyclotomic Polynomials
Pan Tan, Zhengchun Zhou, Haode Yan, Udaya Parampalli · IEEE Communications Letters · 2018
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 Fq, 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 F2to generate binary cyclic LRCs. Our construction extends the earlier one and yields new optimal or almost optimal cyclic LRCs with respect to certain bounds.