English

A Note on the Asymptotic Least Density of Covering Codes in $[q]^n$

Combinatorics 2026-05-20 v1

Abstract

In this short note we revisit the upper bound of the asymptotic least density of covering codes of radius RR in [q]n[q]^n established by Krivelevich, Sudakov, and Vu. We show that by using a slightly different optimization in their core theorem we can obtain a constant factor improvement to their upper bound.

Keywords

Cite

@article{arxiv.2605.19094,
  title  = {A Note on the Asymptotic Least Density of Covering Codes in $[q]^n$},
  author = {Andrey Shapiro},
  journal= {arXiv preprint arXiv:2605.19094},
  year   = {2026}
}

Comments

4 pages