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 >= 2. In this paper, we establish the existence of maximum 2-scattered Fqsubspaces in V (r, q(6)) whenever r >= 3, r not equal 5, and q is an odd power of 2. Additionally, we explore the corresponding MRD codes. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
A new family of 2-scattered subspaces and related MRD codes
Bartoli D.;Ghiandoni F.;
2025
Abstract
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 >= 2. In this paper, we establish the existence of maximum 2-scattered Fqsubspaces in V (r, q(6)) whenever r >= 3, r not equal 5, and q is an odd power of 2. Additionally, we explore the corresponding MRD codes. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
