On the Density of Codes over Finite Chain Rings
Anna-Lena Horlemann, Violetta Weger, Nadja Willenborg
TL;DR
This paper investigates the asymptotic density of certain error-correcting codes over finite chain rings, focusing on free modules with good distance properties, and applies the results to rank and Hamming metric codes.
Contribution
It introduces a method to analyze the asymptotic proportion of codes over finite chain rings with desirable distance features, extending to rank and Hamming metrics.
Findings
Determined asymptotic proportions of free modules with good distance properties
Analyzed the asymptotics in code length and residue field size separately
Applied techniques to rank metric and Hamming metric codes
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.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding