Bounds on Locally Recoverable Codes with Multiple Recovering Sets

A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. Bounds on the rate and distance of such codes have been extensively studied in the literature. In this paper we derive upper bounds on the rate and distance of codes in which every symbol has $t\geq 1$ disjoint recovering sets.