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The generalized covering radii of Melas codes

  • Shuxing Li
  • Maosheng Xiong
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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 ρt(M(m,q)) of Melas codes M(m,q) over any finite field 𝔽q. We determine ρ2(M(m,q)) for all q, and for a general t β‰₯ 3, we prove that ρt(M(m,q)) ∈ {2t,2t+1} for q ∈ {2,3} and ρt(M(m,q))=2t for q β‰₯ 4 whenever m is sufficiently large. These results extend recent work on the covering radius of Melas codes.

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Cite

BibTeXRIS
BibTeX
@misc{li2026generalized,
  title = {{The generalized covering radii of Melas codes}},
  author = {Shuxing Li and Maosheng Xiong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.29906},
  eprint = {2608.29906},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29906},
}
RIS
TY  - UNPB
TI  - The generalized covering radii of Melas codes
AU  - Shuxing Li
AU  - Maosheng Xiong
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2608.29906
UR  - https://arxiv.org/abs/2608.29906
AB  - 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 𝔽_q. We determine ρ_2(M(m,q)) for all q, and for a general t β‰₯ 3, we prove that ρ_t(M(m,q)) ∈ {2t,2t+1} for q ∈ {2,3} and ρ_t(M(m,q))=2t for q β‰₯ 4 whenever m is sufficiently large. These results extend recent work on the covering radius of Melas codes.
ER  -