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arXiv · 1910.02278

A new family of maximum scattered linear sets in $\mathrm{PG}(1,q^6)$

Daniele Bartoli·Corrado Zanella·Ferdinando Zullo
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Abstract

We generalize the example of linear set presented by the last two authors in "Vertex properties of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$" (2019) to a more general family, proving that such linear sets are maximum scattered when $q$ is odd and, apart from a special case, they are are new. This solves an open problem posed in "Vertex properties of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$" (2019). As a consequence of Sheekey's results in "A new family of linear maximum rank distance codes" (2016), this family yields to new MRD-codes with parameters $(6,6,q;5)$.

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Daniele Bartoli, Corrado Zanella, Ferdinando Zullo. 2019-10-05. A new family of maximum scattered linear sets in $\mathrm{PG}(1,q^6)$. https://arxiv.org/abs/1910.02278

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