Abstract
AbstractWe investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including (sub)linear 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications
Reference23 articles.
1. Antrobus J., Gluesing-Luerssen H.: Maximal Ferrers diagram codes: constructions and genericity considerations. IEEE Trans. Inf. Theory 65(10), 6204–6223 (2019).
2. Apostol T.M.: Introduction to Analytic Number Theory. Springer, New York (2013).
3. Baldi M., Battaglioni M., Chiaraluce F., Horlemann-Trautmann A.-L., Persichetti E., Santini P., Weger V.: A new path to code-based signatures via identification schemes with restricted errors (2021)
4. Ball S., Gamboa G., Lavrauw M.: On additive MDS codes over small fields. arXiv:2012.06183 (2020)
5. Barg A., Forney G.D.: Random codes: minimum distances and error exponents. IEEE Trans. Inf. Theory 48(9), 2568–2573 (2002).
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