Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power Hadamard matrices and Plotkin-optimal $p^k$-ary codes   A power Hadamard matrix $H(x)$ is a square matrix of dimension $n$ with
entries from Laurent polynomial ring $L= \mathbb{Q} [x,x^{-1}]$ such that
$H(x)H(x^{-1})^T=nI \mod f(x)$, where $f$ is some Laurent polynomial of degree
greater than $0$. In the first part of this work, some new results on power
Hadamard matrices are studied, where we mainly entend the work of Craigen and
Woodford. In the second part, codes obtained from Butson-Hadamard matrices are
discussed and some bounds on the minimum distance of these codes are proved. In
particular, we show that the code obtained from a Butson-Hadamard matrix meets
the Plotkin bound under a non-homegeneous weight.

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The categories of this paper are: nlin
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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: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics