The generalized covering radii of Melas codes

2026-08-30

AI Summary

本文研究了Melas码的广义覆盖半径问题，通过数学分析方法确定了不同参数下的具体值，扩展了该领域先前的研究成果。

Abstract

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.

Problem

• generalized covering radii
• Melas codes
• finite field

Innovation

• generalized covering radii
• Melas codes
• finite field