English

On the Density of Codes over Finite Chain Rings

Information Theory 2022-12-20 v1 math.IT

Abstract

We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field size q separately. We then specialize and apply our technique to rank metric codes and to Hamming metric codes.

Keywords

Cite

@article{arxiv.2212.09568,
  title  = {On the Density of Codes over Finite Chain Rings},
  author = {Anna-Lena Horlemann and Violetta Weger and Nadja Willenborg},
  journal= {arXiv preprint arXiv:2212.09568},
  year   = {2022}
}