Name
Abstract | ||
|---|---|---|
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the q-analogues of projective systems and blocking sets. We also illustrate how to associate a classical Hamming-metric code to a rank-metric one, in such a way that various rank-metric properties naturally translate into the homonymous Hamming-metric notions under this correspondence. The most interesting applications of our results lie in the theory of minimal rank-metric codes, which we introduce and study from several angles. Our main contributions are bounds for the parameters of a minimal rank-metric codes, a general existence result based on a combinatorial argument, and an explicit code construction for some parameter sets that uses the notion of a scattered linear set. Throughout the paper we also show and comment on curious analogies/divergences between the theories of error-correcting codes in the rank and in the Hamming metric. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.jcta.2022.105658 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
Rank-metric codes,Minimal codes,Linear sets,Linear cutting blocking sets,Projective systems | Journal | 192 |
ISSN | Citations | PageRank |
0097-3165 | 0 | 0.34 |
References | Authors | |
5 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gianira N. Alfarano | 1 | 0 | 0.34 |
| Martino Borello | 2 | 0 | 0.34 |
| Alessandro Neri | 3 | 0 | 0.68 |
| Alberto Ravagnani | 4 | 0 | 0.34 |