“…Upper bounds on the minimum Hamming distance were proved, e.g., Singleton-type bounds [7], [17], [31], [41], and bounds related with the alphabet size [1], [5]. Optimal LRCs (with respect to these bounds), were constructed, e.g., [13], [24], [28], [34], [37], [38], [42]. In [10], [21], lower bounds on the field size of optimal LRCs were derived for δ = 2 [21], and δ 2 [10].…”