Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Programming Bounds for Almost-Balanced Binary Codes   We revisit the linear programming bounds for the size vs. distance trade-off
for binary codes, focusing on the bounds for the almost-balanced case, when all
pairwise distances are between $d$ and $n-d$, where $d$ is the code distance
and $n$ is the block length. We give an optimal solution to Delsarte's LP for
the almost-balanced case with large distance $d \geq (n - \sqrt{n})/2 + 1$,
which shows that the optimal value of the LP coincides with the Grey-Rankin
bound for self-complementary codes.
  We also show that a limitation of the asymptotic LP bound shown by
Samorodnitsky, namely that it is at least the average of the first MRRW upper
bound and Gilbert-Varshamov bound, continues to hold for the almost-balanced
case.

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The categories of this paper are: physics
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The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex