  We investigate the distance properties of linear locally recoverable codes
(LRC codes) with all-symbol locality and availability. New upper and lower
bounds on the minimum distance of such codes are derived. The upper bound is
based on the shortening method and improves existing shortening bounds. To
reduce the gap in between upper and lower bounds we do not restrict the
alphabet size and propose explicit constructions of codes with locality and
availability via rank-metric codes. The first construction relies on expander
graphs and is better in low rate region, the second construction utilizes LRC
codes developed by Wang et al. as inner codes and better in high rate region.
