On the Maximal Code Length of Optimal Linear LRC Codes with Availability

A code over finite alphabet is said to be locally recoverable (LRC) if each code symbol is function of small number of other symbols forming the recovering set [1], [2], [3], [4], [5]. These codes were first proposed in [1] and immediate become popular due to obvious applications in distributed and cloud storage systems. Natural generalization of LRC codes is LRC codes with availability in which each code symbol has more than one disjoint recovering set. A LRC codes with availability is said to be optimal if its minimum distance achieves the Singleton- like bound developed by Kruglik et. al in this paper we study the maximum code length of q-ary optimal LRC with availability and then derive some structural properties.