A new family of linear maximum rank distance codes
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Publication:326326
DOI10.3934/amc.2016019zbMath1348.94087arXiv1504.01581OpenAlexW2963120842MaRDI QIDQ326326
Publication date: 12 October 2016
Published in: Advances in Mathematics of Communications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.01581
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Semifields (12K10)
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Cites Work
- Unnamed Item
- Unnamed Item
- Non-linear maximum rank distance codes
- Rank-metric codes and their duality theory
- Algebraic structures of MRD codes
- Constant rank-distance sets of Hermitian matrices and partial spreads in Hermitian polar spaces
- Symmetric bilinear forms over finite fields with applications to coding theory
- Determination of division algebras with 243 elements
- Generalized twisted Gabidulin codes
- A geometric construction of finite semifields
- Translation dual of a semifield
- Subspaces of matrices with special rank properties
- Galois theory and linear algebra
- Galois extensions and subspaces of alternating bilinear forms with special rank properties
- Theory of codes with maximum rank distance
- On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field
- Bilinear forms over a finite field, with applications to coding theory
- The collineation groups of generalized twisted field planes
- Translation planes of order 27
- Scattered spaces with respect to a spread in \(\text{PG}(n,q)\)
- On embeddings of minimum dimension of \(\mathrm{PG}(n,q)\times \mathrm{PG}(n,q)\)
- Symmetric rank codes
- Generalized twisted fields
- Scattered spaces in Galois geometry
- Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes
- Finite semifields with a large nucleus and higher secant varieties to Segre varieties
- Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4
- Isometries for rank distance and permutation group of gabidulin codes
- Coding for Errors and Erasures in Random Network Coding
- A Rank-Metric Approach to Error Control in Random Network Coding
- On a Special Class of Polynomials
- Constant-Rank Codes and Their Connection to Constant-Dimension Codes
- Blocking sets and derivable partial spreads
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