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