  A single unicast index coding problem (SUICP) with symmetric neighboring
interference (SNI) has $K$ messages and $K$ receivers, the $k$th receiver
$R_{k}$ wanting the $k$th message $x_{k}$ and having the interference with $D$
messages after and $U$ messages before its desired message. Maleki, Cadambe and
Jafar studied SUICP(SNI) because of its importance in topological interference
management problems. Maleki \textit{et. al.} derived the lowerbound on the
broadcast rate of this setting to be $D+1$. In our earlier work, for SUICP(SNI)
with arbitrary $K,D$ and $U$, we defined set $\mathbf{S}$ of 2-tuples and for
every $(a,b) \in \mathbf{S}$, we constructed $b$-dimensional vector linear
index code with rate $D+1+\frac{a}{b}$ by using an encoding matrix of dimension
$Kb \times (b(D+1)+a)$. In this paper, we use the symmetric structure of the
SUICP(SNI) to reduce the size of encoding matrix by partitioning the message
symbols. The rate achieved in this paper is same as that of the existing
constructions of vector linear index codes. More specifically, we construct
$b$-dimensional vector linear index codes for SUICP(SNI) by partitioning the
$Kb$ messages into $b(U+1)+c$ sets for some non-negative integer $c$. We use an
encoding matrix of size $\frac{Kb}{b(U+1)+c} \times \frac{b(D+1)+a}{b(U+1)+c}$
to encode each partition separately. The advantage of this method is that the
receivers need to store atmost $\frac{b(D+1)+a}{b(U+1)+c}$ number of broadcast
symbols (index code symbols) to decode a given wanted message symbol. We also
give a construction of scalar linear index codes for SUICP(SNI) with arbitrary
$K,D$ and $U$. We give an improved upperbound on the braodcast rate of
SUICP(SNI).
