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MiS Preprint

Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric

Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri and Alberto Ravagnani


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.

Feb 11, 2022
Feb 14, 2022
rank-metric codes, minimal codes, linear sets, linear cutting blocking sets, blocking sets

Related publications

2022 Journal Open Access
Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri and Alberto Ravagnani

Linear cutting blocking sets and minimal codes in the rank metric

In: Journal of combinatorial theory / A, 192 (2022), p. 105658