A new family of 2-scattered subspaces and related MRD codes

作     者：Bartoli, Daniele Ghiandoni, Francesco Giannoni, Alessandro Marino, Giuseppe 

作者机构：Univ Perugia Dipartimento Matemat & Informat Perugia Italy Univ Firenze Dipartimento Matemat & Informat Ulisse Dini Florence Italy Univ Napoli Federico II Dipartimento Matemat & Applicazioni R Caccioppoli Naples Italy 

出 版 物：《FINITE FIELDS AND THEIR APPLICATIONS》 (Finite Fields Appl.)

年 卷 期：2025年第103卷

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：GNSAGA-INdAM 

主　　题：Linearized polynomial Scattered subspaces Rank metric code 

摘      要：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://***/licenses/by-nc-nd/4.0/).