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Linear cutting blocking sets and minimal codes in the rank metric.
- Source :
-
Journal of Combinatorial Theory - Series A . Nov2022, Vol. 192, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 192
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 158675518
- Full Text :
- https://doi.org/10.1016/j.jcta.2022.105658