On Optimal Locally Repairable Codes with Super-Linear Length
Abstract
Locally repairable codes which are optimal with respect to the bound
presented by Prakash et al. are considered. New upper bounds on the length of
such optimal codes are derived. The new bounds both improve and generalize
previously known bounds. Optimal codes are constructed, whose length is
order-optimal when compared with the new upper bounds. The length of the codes
is super-linear in the alphabet size.