  In this work, we consider a slight variant of well known coded caching
problem, referred as multi-access coded caching problem, where each user has
access to $z$ neighboring caches in a cyclic wrap-around way. We present a
placement and delivery scheme for this problem, under the restriction of
uncoded placement. Our work is a generalization of one of the cases considered
in "Multi-access coded caching : gains beyond cache-redundancy" by B. Serbetci,
E. Parrinello and P. Elia. To be precise, when our scheme is specialized to
$z=\frac{K-1}{K \gamma }$, for any $K \gamma$, where $K$ is the number of users
and $\gamma $ is the normalized cache size, we show that our result coincides
with their result. We show that for the cases considered in this work, our
scheme outperforms the scheme proposed in "Rate-memory trade-off for
multi-access coded caching with uncoded placement" by K. S. Reddy and N.
Karamchandani, except for some special cases considered in that paper. We also
show that for $z= K-1$, our scheme achieves the optimal transmission rate.
