  A code is called $(n, k, r, t)$ information symbol locally repairable code
\big($(n, k, r, t)_i$ LRC\big) if each information coordinate can be achieved
by at least $t$ disjoint repair sets, containing at most $r$ other coordinates.
This paper considers a class of $(n, k, r, t)_i$ LRCs, where each repair set
contains exactly one parity coordinate. We explore the systematic code in terms
of the standard parity check matrix. First, some structural features of the
parity check matrix are proposed by showing some connections with the
membership matrix and the minimum distance optimality of the code. Next to
that, parity check matrix based proofs of various bounds associated with the
code are placed. In addition to this, we provide several constructions of
optimal $(n, k, r, t)_i$ LRCs, with the help of two Cayley tables of a finite
field. Finally, we generalize a result of $q$-ary $(n, k, r)$ LRCs to $q$-ary
$(n, k, r, t)$ LRCs.
