A new family of $2$-scattered subspaces and related MRD codes
<|reference_start|>A new family of $2$-scattered subspaces and related MRD codes: Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In this paper, we establish the existence of maximum $2$-scattered $\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd power of $2$. Additionally, we explore the corresponding MRD codes.<|reference_end|>
@article{bartoli2024a,
    title={A new family of $2$-scattered subspaces and related MRD codes},
    author={Daniele Bartoli and Francesco Ghiandoni and Alessandro Giannoni and
  Giuseppe Marino},
    journal={arXiv preprint arXiv:2403.01506},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01506},
    primaryClass={math.CO cs.IT math.IT}
}