  Locally recoverable codes (LRCs) were proposed for the recovery of data in
distributed and cloud storage systems about nine years ago. A lot of progress
on the study of LRCs has been made by now. However, there is a lack of general
theory on the minimum linear locality of linear codes. In addition, the minimum
linear locality of many known families of linear codes is not studied in the
literature. Motivated by these two facts, this paper develops some general
theory about the minimum linear locality of linear codes, and investigates the
minimum linear locality of a number of families of linear codes, such as
$q$-ary Hamming codes, $q$-ary Simplex codes, generalized Reed-Muller codes,
ovoid codes, maximum arc codes, the extended hyperoval codes, and near MDS
codes. Many classes of both distance-optimal and dimension-optimal LRCs are
presented in this paper. The minimum linear locality of many families of linear
codes are settled with the general theory developed in this paper.
