A new family of maximum scattered linear sets in PG(1, q6)

Daniele Bartoli, Corrado Zanella, Ferdinando Zullo

Abstract


We generalize the example of linear set presented by the last two authors in “Vertex properties of maximum scattered linear sets of PG(1, qn)" (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 new. This solves an open problem posed in “Vertex properties of maximum scattered linear sets of PG(1, qn)" (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).


Keywords


Scattered linear set, MRD-code, linearized polynomial

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DOI: https://doi.org/10.26493/1855-3974.2137.7fa

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications