Cyclic LRC codes with hierarchy and availability

Locally recoverable (LRC) codes and their variants have been extensively studied in recent years. In this paper we focus on cyclic LRC codes, presenting two results regarding codes with hierarchical locality and codes with availability. Regarding hierarchical LRC codes, we observe that the cyclic codes of Tamo et al. (2016) can be generalized to yield optimal families with multiple levels of locality for a broader range of parameters than known previously. We also observe that the general approach to cyclic codes with locality can be extended to multidimensional cyclic codes, yielding new families of LRC codes with availability.