On the Density of Codes over Finite Chain Rings

Published 19 Dec 2022 in cs.IT and math.IT | (2212.09568v1)

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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