Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A large family of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$
  and their associated MRD codes   The concept of linear set in projective spaces over finite fields was
introduced by Lunardon in 1999 and it plays central roles in the study of
blocking sets, semifields, rank-distance codes and etc. A linear set with the
largest possible cardinality and rank is called maximum scattered. Despite two
decades of study, there are only a limited number of maximum scattered linear
sets of a line $\mathrm{PG}(1,q^n)$. In this paper, we provide a large family
of new maximum scattered linear sets over $\mathrm{PG}(1,q^n)$ for any even
$n\geq 6$ and odd $q$. In particular, the relevant family contains at least
  \[ \begin{cases}
  \left\lfloor\frac{q^t+1}{8rt}\right\rfloor,& \text{ if }t\not\equiv
2\pmod{4};\\[8pt]
  \left\lfloor\frac{q^t+1}{4rt(q^2+1)}\right\rfloor,& \text{ if }t\equiv
2\pmod{4},
  \end{cases} \]
  inequivalent members for given $q=p^r$ and $n=2t>8$, where
$p=\mathrm{char}(\mathbb{F}_q)$. This is a great improvement of previous
results: for given $q$ and $n>8$, the number of inequivalent maximum scattered
linear sets of $\mathrm{PG}(1,q^n)$ in all classes known so far, is smaller
than $q^2$. Moreover, we show that there are a large number of new maximum
rank-distance codes arising from the constructed linear sets.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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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: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con