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Article Dans Une Revue Journal of Combinatorial Theory, Series A Année : 2022

Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric

Résumé

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.
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Dates et versions

hal-03852310 , version 1 (14-11-2022)

Identifiants

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Gianira Alfarano, Martino Borello, Alessandro Neri, Alberto Ravagnani. Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric. Journal of Combinatorial Theory, Series A, 2022, 192, pp.105658. ⟨10.1016/j.jcta.2022.105658⟩. ⟨hal-03852310⟩
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