  In this paper, we study shared cache coded caching (SC-CC): a set of caches
serves a larger set of users; each user access one cache, and a cache may serve
many users. For this problem, under uncoded placement, Parrinello, \"Unsal, and
Elia showed an optimal SC-CC scheme, in which the subpacketization level
depends upon the number of caches. We show an SC-CC scheme where the
subpacketization level does not directly depend upon the number of users or
caches; any number of caches and users can be accommodated for a fixed
subpacketization level. Furthermore, new caches can be added without re-doing
the placement of the existing caches. We show that given an upper limit on the
allowable subpacketization level, our SC-CC scheme may achieve a lesser rate
than other relevant SC-CC schemes. Our scheme is constructed using matrices and
designs. A matroid can be obtained from a matrix over a finite field; the
placement of our scheme is decided by a design constructed from a matrix; the
circuits of a matroid obtained from the matrix and the design is used to decide
the delivery.
