New criteria for MRD and Gabidulin codes and some rank-metric code constructions
From MaRDI portal
Publication:2408283
DOI10.3934/amc.2017042zbMath1431.94151arXiv1507.08641OpenAlexW3105173723MaRDI QIDQ2408283
Anna-Lena Horlemann-Trautmann, Kyle Marshall
Publication date: 12 October 2017
Published in: Advances in Mathematics of Communications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.08641
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05)
Related Items (28)
Extending two families of maximum rank distance codes ⋮ Exceptional scattered polynomials ⋮ Explicit constructions of some non-Gabidulin linear maximum rank distance codes ⋮ Automorphism groups of Gabidulin-like codes ⋮ On the number of inequivalent Gabidulin codes ⋮ On kernels and nuclei of rank metric codes ⋮ Nuclei and automorphism groups of generalized twisted Gabidulin codes ⋮ Identifiers for MRD-codes ⋮ Systematic maximum sum rank codes ⋮ Cryptanalysis and repair of a Gabidulin code based cryptosystem from ACISP 2018 ⋮ Constructions of optimal rank-metric codes from automorphisms of rational function fields ⋮ New semifields and new MRD codes from skew polynomial rings ⋮ Some matroids related to sum-rank metric codes ⋮ Concatenation of convolutional codes and rank metric codes for multi-shot network coding ⋮ Extension of Overbeck's attack for Gabidulin-based cryptosystems ⋮ On the genericity of maximum rank distance and Gabidulin codes ⋮ Equivalence and characterizations of linear rank-metric codes based on invariants ⋮ Some new non-additive maximum rank distance codes ⋮ Matrix graphs and MRD codes over finite principal ideal rings ⋮ A new McEliece-type cryptosystem using Gabidulin-Kronecker product codes ⋮ Classification of large partial plane spreads in \(\mathrm{PG}(6,2)\) and related combinatorial objects ⋮ Vertex properties of maximum scattered linear sets of \(\mathrm{PG} ( 1 , q^n )\) ⋮ Random construction of partial MDS codes ⋮ Systematic encoders for generalized Gabidulin codes and the \(q\)-analogue of Cauchy matrices ⋮ MRD codes with maximum idealizers ⋮ Theory of supports for linear codes endowed with the sum-rank metric ⋮ New rank codes based encryption scheme using partial circulant matrices ⋮ Rank-Metric Codes and Their Applications
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Non-linear maximum rank distance codes
- A new family of linear maximum rank distance codes
- Algebraic structures of MRD codes
- Galois invariance, trace codes and subfield subcodes
- Theory of codes with maximum rank distance
- Bilinear forms over a finite field, with applications to coding theory
- Extension of Overbeck's attack for Gabidulin-based cryptosystems
- Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes
- Isometries for rank distance and permutation group of gabidulin codes
- Designing a Rank Metric Based McEliece Cryptosystem
This page was built for publication: New criteria for MRD and Gabidulin codes and some rank-metric code constructions
