Cyclic and convolutional codes with locality [article]

Zitan Chen, Alexander Barg
2020 arXiv   pre-print
Locally recoverable (LRC) codes and their variants have been extensively studied in recent years. In this paper we focus on cyclic constructions of LRC codes and derive conditions on the zeros of the code that support the property of hierarchical locality. As a result, we obtain a general family of hierarchical LRC codes for a new range of code parameters. We also observe that our approach enables one to represent an LRC code in quasicyclic form, and use this representation to construct
more » ... ing convolutional LRC codes with locality. Among other results, we extend the general approach to cyclic codes with locality to multidimensional cyclic codes, yielding new families of LRC codes with availability, and construct a family of q-ary cyclic hierarchical LRC codes of unbounded length.
arXiv:2004.06770v1 fatcat:uzu2jxeo5zc7lj2dy5zimqokua