Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight distribution of random linear codes and Krawchouk polynomials   For $0 < \lambda < 1$ and $n \rightarrow \infty$ pick uniformly at random
$\lambda n$ vectors in $\{0,1\}^n$ and let $C$ be the orthogonal complement of
their span. Given $0 < \gamma < \frac12$ with $0 < \lambda < h(\gamma)$, let
$X$ be the random variable that counts the number of words in $C$ of Hamming
weight $i = \gamma n$ (where $i$ is assumed to be an even integer). Linial and
Mosheiff determined the asymptotics of the moments of $X$ of all orders
$o\left(\frac{n}{\log n}\right)$. In this paper we extend their estimates up to
moments of linear order. Our key observation is that the behavior of the
suitably normalized $k^{th}$ moment of $X$ is essentially determined by the
$k^{th}$ norm of the Krawchouk polynomial $K_i$.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin