Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $Z_4$-codes and their Gray map images as orthogonal arrays   A classic result of Delsarte connects the strength (as orthogonal array) of a
linear code with the minimum weight of its dual: the former is one less than
the latter. We show that Delsarte's observation extends to codes over arbitrary
finite rings.
  Since the paper of Hammons \emph{et al.}, there is a lot of interest in codes
over rings, especially in codes over $Z_4$ and their (usually non-linear)
binary Gray map images.
  We show that Delsarte's observation extends to codes over arbitrary finite
commutative rings with identity. Also, we show that the strength of the Gray
map image of a $Z_4$ code is one less than the minimum Lee weight of its Gray
map image.

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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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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: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin