RS-like locally recoverable codes with intersecting recovering sets

Abstract

A recovering set for a coordinate position i in a code is a set Ri of other coordinate positions such that the value at the ith position can be recovered by accessing the values at coordinate positions in Ri. A locally recoverable (LRC) code with multiple recovering sets is a code in which for every coordinate position there are more than one recovering set. Such codes have been generally studied with the assumption that the recovering sets are pairwise disjoint. Recently Kruglik et al. [1] have presented a construction of LRC codes in which the recovering sets of a coordinate need not be disjoint. In this paper, we present a construction of such type of codes by using the construction of RS-like LRC codes. Further, using a bound given in [1], we have obtained a bound on the rate of the codes from the present construction. Also, we have presented a sufficient condition for a cyclic code over a finite field to be an LRC code with intersecting recovering sets.