Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted Centralizer Codes   Given an $n\times n$ matrix $A$ over a field $F$ and a scalar $a\in F$, we
consider the linear codes $C(A,a):=\{B\in F^{n\times n}\mid \,AB=aBA\}$ of
length $n^2$. We call $C(A,a)$ a twisted centralizer code. We investigate
properties of these codes including their dimensions, minimum distances,
parity-check matrices, syndromes, and automorphism groups. The minimal distance
of a centralizer code (when $a=1$) is at most $n$, however for $a\ne 0,1$ the
minimal distance can be much larger, as large as $n^2$.

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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex