Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full-Rank Perfect Codes over Finite Fields   In this paper, we propose a construction of full-rank q-ary 1-perfect codes
over finite fields. This construction is a generalization of the Etzion and
Vardy construction of full-rank binary 1-perfect codes (1994). Properties of
i-components of q-ary Hamming codes are investigated and the construction of
full-rank q-ary 1-perfect codes is based on these properties. The switching
construction of 1-perfect codes are generalized for the q-ary case. We give a
generalization of the concept of i-component of 1-perfect codes and introduce
the concept of (i,{\sigma})-components of q-ary 1-perfect codes. We also
present a generalization of the Lindstr\"om and Sch\"onheim construction of
q-ary 1-perfect codes and provide a lower bound on the number of pairwise
distinct q-ary 1-perfect codes of length n.

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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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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: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org