Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Codes with the Identifiable Parent Property for Multimedia
  Fingerprinting   Let ${\cal C}$ be a $q$-ary code of length $n$ and size $M$, and ${\cal C}(i)
= \{{\bf c}(i) \ | \ {\bf c}=({\bf c}(1), {\bf c}(2), \ldots, {\bf c}(n))^{T}
\in {\cal C}\}$ be the set of $i$th coordinates of ${\cal C}$. The descendant
code of a sub-code ${\cal C}^{'} \subseteq {\cal C}$ is defined to be ${\cal
C}^{'}(1) \times {\cal C}^{'}(2) \times \cdots \times {\cal C}^{'}(n)$. In this
paper, we introduce a multimedia analogue of codes with the identifiable parent
property (IPP), called multimedia IPP codes or $t$-MIPPC$(n, M, q)$, so that
given the descendant code of any sub-code ${\cal C}^{'}$ of a multimedia
$t$-IPP code ${\cal C}$, one can always identify, as IPP codes do in the
generic digital scenario, at least one codeword in ${\cal C}^{'}$. We first
derive a general upper bound on the size $M$ of a multimedia $t$-IPP code, and
then investigate multimedia $3$-IPP codes in more detail. We characterize a
multimedia $3$-IPP code of length $2$ in terms of a bipartite graph and a
generalized packing, respectively. By means of these combinatorial
characterizations, we further derive a tight upper bound on the size of a
multimedia $3$-IPP code of length $2$, and construct several infinite families
of (asymptotically) optimal multimedia $3$-IPP codes of length $2$.

30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas