Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced Dimensional Optimal Vector Linear Index Codes for Index Coding
  Problems with Symmetric Neighboring and Consecutive Side-information   A single unicast index coding problem (SUICP) with symmetric neighboring and
consecutive side-information (SNCS) has $K$ messages and $K$ receivers, the
$k$th receiver $R_k$ wanting the $k$th message $x_k$ and having the
side-information $\mathcal{K}_k=\{x_{k-U},\dots,x_{k-2},x_{k-1}\}\cup\{x_{k+1},
x_{k+2},\dots,x_{k+D}\}$. The single unicast index coding problem with
symmetric neighboring and consecutive side-information, SUICP(SNCS), is
motivated by topological interference management problems in wireless
communication networks. Maleki, Cadambe and Jafar obtained the symmetric
capacity of this SUICP(SNCS) and proposed optimal length codes by using
Vandermonde matrices. In our earlier work, we gave optimal length
$(U+1)$-dimensional vector linear index codes for SUICP(SNCS) satisfying some
conditions on $K,D$ and $U$ \cite{VaR1}. In this paper, for SUICP(SNCS) with
arbitrary $K,D$ and $U$, we construct optimal length
$\frac{U+1}{\text{gcd}(K,D-U,U+1)}$-dimensional vector linear index codes. We
prove that the constructed vector linear index code is of minimal dimension if
$\text{gcd}(K-D+U,U+1)$ is equal to $\text{gcd}(K,D-U,U+1)$. The proposed
construction gives optimal length scalar linear index codes for the SUICP(SNCS)
if $(U+1)$ divides both $K$ and $D-U$. The proposed construction is independent
of field size and works over every field. We give a low-complexity decoding for
the SUICP(SNCS). By using the proposed decoding method, every receiver is able
to decode its wanted message symbol by simply adding some index code symbols
(broadcast symbols).

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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th