Application of optimal p-ary linear codes to alphabet-optimal locally repairable codes

Linear codes have widespread applications in data storage systems. There are two major contributions in this paper. We first propose infinite families of optimal or distance-optimal linear codes over Fp constructed from projective spaces.Moreover, a necessary and sufficient condition for such linear codes to be Griesmer codes is presented. Secondly, as an application in data storage systems, we investigate the locality of the linear codes constructed. Furthermore, we show that these linear codes are alphabet-optimal locally repairable codes with locality 2.Nanyang Technological UniversitySubmitted/Accepted versionThis work was supported by NTU Research Grant 04INS000047C230GRT01