Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semidefinite bounds for nonbinary codes based on quadruples   For nonnegative integers $q,n,d$, let $A_q(n,d)$ denote the maximum
cardinality of a code of length $n$ over an alphabet $[q]$ with $q$ letters and
with minimum distance at least $d$. We consider the following upper bound on
$A_q(n,d)$. For any $k$, let $\CC_k$ be the collection of codes of cardinality
at most $k$. Then $A_q(n,d)$ is at most the maximum value of
$\sum_{v\in[q]^n}x(\{v\})$, where $x$ is a function $\CC_4\to R_+$ such that
$x(\emptyset)=1$ and $x(C)=0$ if $C$ has minimum distance less than $d$, and
such that the $\CC_2\times\CC_2$ matrix $(x(C\cup C'))_{C,C'\in\CC_2}$ is
positive semidefinite. By the symmetry of the problem, we can apply
representation theory to reduce the problem to a semidefinite programming
problem with order bounded by a polynomial in $n$. It yields the new upper
bounds $A_4(6,3)\leq 176$, $A_4(7,4)\leq 155$, $A_5(7,4)\leq 489$, and
$A_5(7,5)\leq 87$.

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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th