  Index coding employs coding across clients within the same broadcast domain.
This typically assumes that all clients learn the coding matrix so that they
can decode and retrieve their requested data. However, learning the coding
matrix can pose privacy concerns: it may enable clients to infer information
about the requests and side information of other clients [1]. In this paper, we
formalize the intuition that the achieved privacy can increase by decreasing
the number of rows of the coding matrix that a client learns. Based on this, we
propose the use of $k$-limited-access schemes: given an index coding scheme
that employs $T$ transmissions, we create a $k$-limited-access scheme with
$T_k\geq T$ transmissions, and with the property that each client learns at
most $k$ rows of the coding matrix to decode its message. We derive upper and
lower bounds on $T_k$ for all values of $k$, and develop deterministic designs
for these schemes for which $T_k$ has an order-optimal exponent for some
regimes.
