@article{0a07bab3ba974113abc63d53b22ca181,
title = "Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces",
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. ",
keywords = "cs.IT, cs.DM, math.IT, Hamming metric, Sum-rank metric, Gilbert–Varshamov bound, Rank metric, Graph theory, Sublinear codes, Singleton-type bound, Asymptotic density",
author = "Anina Gruica and Anna-Lena Horlemann and Alberto Ravagnani and Nadja Willenborg",
year = "2024",
month = mar,
doi = "10.1007/s10623-023-01236-2",
language = "English",
volume = "92",
pages = "609--637",
journal = "Designs, Codes and Cryptography",
issn = "0925-1022",
publisher = "Springer",
number = "3",
}