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

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 $(6,6,q;5)$.

References in corpus (8)

• On kernels and nuclei of rank metric codes
• A characterization of linearized polynomials with maximum kernel
• Vertex properties of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$
• Scalar $q$-subresultants and Dickson matrices
• Identifiers for MRD-codes
• Towards the full classification of exceptional scattered polynomials
• MRD-codes arising from the trinomial $x^q+x^{q^3}+c{x}^{q^5}\in {\mathbb{F}}_{q^6}[x]$
• Maximum scattered linear sets and MRD-codes

Cited by in corpus (1)

• Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants