Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced Weighing Matrices   A unified approach to the construction of weighing matrices and certain
symmetric designs is presented. Assuming the weight $p$ in a weighing matrix
$W(n,p)$ is a prime power, it is shown that there is a
$$W\left(\frac{p^{m+1}-1}{p-1}(n-1)+1,p^{m+1}\right)$$ for each positive
integer $m$. The case of $n=p+1$ reduces to the balanced weighing matrices with
classical parameters $$W\left(\frac{p^{m+2}-1}{p-1},p^{m+1}\right).$$ The
equivalence with certain classes of association schemes is discussed in
details.

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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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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-bio
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol