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arXiv · 2208.10573

Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces

Anina Gruica·Anna-Lena Horlemann·Alberto Ravagnani·Nadja Willenborg
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Abstract

We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric spaces, and then specialize our results to the Hamming metric, to the rank metric, and to the sum-rank metric. Our results show that the asymptotic density of codes heavily depends on the imposed linearity degree and the chosen metric.

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Anina Gruica, Anna-Lena Horlemann, Alberto Ravagnani, Nadja Willenborg. 2022-08-22. Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces. https://doi.org/10.1007/s10623-023-01236-2

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