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}
}