The Constructions Of Optimal Cyclic Locally Repairable Codes Based On Their Zeros

In distributed storage systems,locally repairable codes（LRCs）are widely used in data storage and repair of failed nodes.In recent years,many researches have focused on using cyclic codes to construct optimal（r,δ）LRC.Most of them construct the optimal cyclic LRCs by selecting the zeros of the generator polynomial.Fuyin Tian and Shixin Zhu constructed two classes of optimal cyclic（r,δ）LRCs with unbounded length under the condition of（r+δ-1）|（q+1）for odd and even cases ofδ.Inspired by the above results,this thesis modifies the parameters of the above two classes of constructions.Compared with their constructions,the minimum distance of our constructions can reach d=2δwhenδis odd and the parameterρ₁for the length n only needs to satisfy the condition gcd（ρ₁,r+δ-1）|（q-1）whenδis even.