Optimal Cyclic Locally Repairable Codes via Cyclotomic Polynomials
Pan Tan, Zhengchun Zhou, Haode Yan, Udaya Parampalli
IEEE COMMUNICATIONS LETTERS | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Published : 2019
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 q , 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 2 to generate binary cyclic LRCs. Our construction extends the earlier one and yields new optimal or almost optimal cyclic LRCs with r..View full abstract
Awarded by National Science Foundation of China
Awarded by application fundamental research plan project of Sichuan Province
This work was supported in part by the National Science Foundation of China under Grants 61672028, in part by the application fundamental research plan project of Sichuan Province under Grant 2018JY0046, and in part by the University of Melbourne's Communications Coding and Sensing research Consortium of IRRTF fund.