Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds and Constructions for $\overline{3}$-Strongly Separable Codes
  with Length $3$   As separable code (SC, IEEE Trans Inf Theory 57:4843-4851, 2011) and
frameproof code (FPC, IEEE Trans Inf Theory 44:1897-1905, 1998) do in
multimedia fingerprinting, strongly separable code (SSC, Des. Codes and
Cryptogr.79:303-318, 2016) can be also used to construct anti-collusion codes.
Furthermore, SSC is better than FPC and SC in the applications for multimedia
fingerprinting since SSC has lower tracing complexity than that of SC (the same
complexity as FPC) and weaker structure than that of FPC. In this paper, we
first derive several upper bounds on the number of codewords of
$\overline{t}$-SSC. Then we focus on $\overline{3}$-SSC with codeword length
$3$, and obtain the following two main results: (1) An equivalence between an
SSC and an SC. %Consequently a more tighter upper bound $(3q^2/4)$ and lower
bound $(q^{3/2})$ on the number of codewords are obtained; (2) An improved
lower bound $\Omega (q^{5/3}+q^{4/3}-q)$ on the size of a $q$-ary SSC when
$q=q_1^6$ for any prime power $q_1\equiv\ 1 \pmod 6$, better than the before
known bound $\lfloor\sqrt{q}\rfloor^{3}$, which is obtained by means of
difference matrix and the known result on the subset of $\mathbb{F}^{n}_q$
containing no three points on a line.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex