Non-linear maximum rank distance codes

DOI10.1007/s10623-015-0108-0zbMath1386.94112OpenAlexW2175076659MaRDI QIDQ281322

Francesco Pavese, Giuseppe Marino, Antonio Cossidente

Publication date: 10 May 2016

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-015-0108-0

zbMATH Keywords

Singer cyclic groupSegre varietysubspace codesconstant rank distance codemaximum rank distance codeVeronese variety

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Other types of codes (94B60) Combinatorial structures in finite projective spaces (51E20) Projective techniques in algebraic geometry (14N05)

Related Items (24)

Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries ⋮ Self-duality of generalized twisted Gabidulin codes ⋮ Constructions of rank metric codes under actions of the unitary groups ⋮ Exceptional scattered polynomials ⋮ A new family of linear maximum rank distance codes ⋮ On the number of inequivalent Gabidulin codes ⋮ MRD-codes arising from the trinomial \(x^q + x^{q^3} + c x^{q^5} \in \mathbb{F}_{q^6} [x\)] ⋮ On kernels and nuclei of rank metric codes ⋮ New criteria for MRD and Gabidulin codes and some rank-metric code constructions ⋮ On absolute points of correlations of \(\mathrm{PG}(2,q^{n})\) ⋮ Nuclei and automorphism groups of generalized twisted Gabidulin codes ⋮ Identifiers for MRD-codes ⋮ New semifields and new MRD codes from skew polynomial rings ⋮ On the genericity of maximum rank distance and Gabidulin codes ⋮ Some new non-additive maximum rank distance codes ⋮ Matrix graphs and MRD codes over finite principal ideal rings ⋮ Generalized bilinear forms graphs and MRD codes over a residue class ring ⋮ A generalization of the normal rational curve in \(\mathrm {PG}(d,q^n)\) and its associated non-linear MRD codes ⋮ Generalized twisted Gabidulin codes ⋮ On the sparseness of certain linear MRD codes ⋮ Puncturing maximum rank distance codes ⋮ MRD codes with maximum idealizers ⋮ An asymptotically optimal construction of almost affinely disjoint subspaces ⋮ Binary additive MRD codes with minimum distance \(n-1\) must contain a semifield spread set

Uses Software

• Magma

Cites Work

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