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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2022

Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric

Eduardo Camps Moreno
  • Fonction : Auteur
Elisa Gorla
  • Fonction : Auteur
Cristina Landolina
  • Fonction : Auteur
Elisa Lorenzo García
  • Fonction : Auteur
Umberto Martínez-Peñas
  • Fonction : Auteur
Flavio Salizzoni
  • Fonction : Auteur

Résumé

Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric. In this paper, we provide an Anticode Bound for the sum-rank metric, which extends the corresponding Hamming and rank-metric Anticode bounds. We classify then optimal anticodes, i.e., codes attaining the sum-rank metric Anticode Bound. We use these optimal anticodes to define generalized sum-rank weights and we study their main properties. In particular, we prove that the generalized weights of an MSRD code are determined by its parameters. As an application, in the Appendix we explain how generalized weights measure information leakage in multishot network coding.

Dates et versions

hal-03505675 , version 1 (31-12-2021)

Identifiants

Citer

Elisa Lorenzo García, Eduardo Camps Moreno, Elisa Gorla, Cristina Landolina, Elisa Lorenzo García, et al.. Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric. IEEE Transactions on Information Theory, 2022, 68 (Issue: 6), pp.3806 - 3822. ⟨hal-03505675⟩
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