发表机构
University of Delaware; The Hong Kong University of Science and Technology（特拉华大学; 香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究任意有限域上Melas码的广义覆盖半径，确定了ρ_2(M(m,q))，对t≥3分q∈{2,3}和q≥4两种情况得出ρ_t(M(m,q))的取值，扩展了Melas码覆盖半径的相关研究。
AI 中文摘要
广义覆盖半径近来已成为线性码的基本参数，可应用于数据库线性查询。本文研究任意有限域𝔽_q上Melas码M(m,q)的广义覆盖半径ρ_t(M(m,q))，确定了所有q对应的ρ_2(M(m,q))；对t≥3，证明当q∈{2,3}且m足够大时，ρ_t(M(m,q))∈{2t,2t+1}，当q≥4且m足够大时，ρ_t(M(m,q))=2t，这些结果扩展了近期关于Melas码覆盖半径的研究工作。
英文摘要
The generalized covering radii have recently emerged as fundamental parameters of linear codes with applications to database linear querying. In this paper, we study the generalized covering radii $ρ_t(M(m,q))$ of Melas codes $M(m,q)$ over any finite field $\mathbb{F}_q$. We determine $ρ_2(M(m,q))$ for all $q$, and for a general $t \ge 3$, we prove that $ρ_t(M(m,q)) \in \left\{2t,2t+1\right\}$ for $q \in \{2,3\}$ and $ρ_t(M(m,q))=2t$ for $q \ge 4$ whenever $m$ is sufficiently large. These results extend recent work on the covering radius of Melas codes.
CommentsWe have updated the references to reflect recent literature on this topic. In addition, we have clarified the relationship between our work and a related in-press article by another group, which addressed the binary Melas codes
