On kernels and nuclei of rank metric codes
From MaRDI portal
Publication:2408108
DOI10.1007/s10801-017-0755-5zbMath1392.94953arXiv1606.02541OpenAlexW2413632333MaRDI QIDQ2408108
Yue Zhou, Guglielmo Lunardon, Rocco Trombetti
Publication date: 9 October 2017
Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.02541
Related Items
Equivalence, group of automorphism and invariants of a family of rank metric codes arising from linearized polynomials ⋮ Extending two families of maximum rank distance codes ⋮ 50 years of translation structures ⋮ Exceptional scattered polynomials ⋮ 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 equivalence of maximum additive symmetric rank-distance codes ⋮ Nuclei and automorphism groups of generalized twisted Gabidulin codes ⋮ Identifiers for MRD-codes ⋮ On the equivalence issue of a class of 2-dimensional linear maximum rank distance codes ⋮ Rank-Metric Codes, Semifields, and the Average Critical Problem ⋮ Codes with few weights arising from linear sets ⋮ New semifields and new MRD codes from skew polynomial rings ⋮ On a family of linear MRD codes with parameters \([8\times 8,16,7_q\)] ⋮ On the classification of exceptional scattered polynomials ⋮ Linearized trinomials with maximum kernel ⋮ Partially scattered linearized polynomials and rank metric codes ⋮ Classes and equivalence of linear sets in \(\mathrm{PG}(1,q^{n})\) ⋮ A new family of MRD-codes ⋮ Linear sets and MRD-codes arising from a class of scattered linearized polynomials ⋮ New maximum scattered linear sets of the projective line ⋮ Scattered subspaces and related codes ⋮ On maximum additive Hermitian rank-metric codes ⋮ Rank-metric codes, linear sets, and their duality ⋮ MRD codes with maximum idealizers ⋮ A new family of maximum scattered linear sets in PG(1, q^6) ⋮ Asymptotics of Moore exponent sets
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Non-linear maximum rank distance codes
- Switchings of semifield multiplications
- Bilinear dual hyperovals from binary commutative presemifields
- A new family of linear maximum rank distance codes
- Algebraic structures of MRD codes
- Automorphism groups of Gabidulin-like codes
- New dimensional dual hyperovals, which are not quotients of the classical dual hyperovals
- Symmetric doubly dual hyperovals have an odd rank
- MRD-codes and linear sets
- Desarguesian spreads
- Towards the classification of rank 2 semifields 6-dimensional over their center
- Generalized twisted Gabidulin codes
- Über Parallelstrukturen. I: Grundbegriffe. II: Translationsstrukturen. III: Zentrale \(t\)-Strukturen
- Almost perfect and planar functions
- Dimensional dual hyperovals associated with quadratic APN functions
- Constructing new APN functions from known ones
- On the duals of certain \(d\)-dimensional dual hyperovals in \(\mathrm{PG}(2d+1,2)\)
- 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
- \(n\)-dimensional algebras over a field with a cyclic extension of degree \(n\)
- Ambient spaces of dimensional dual arcs
- A new family of semifields with 2 parameters
- Dimensional doubly dual hyperovals and bent functions
- Dimensional dual hyperovals and APN functions with translation groups
- Orthogonal dual hyperovals, symplectic spreads, and orthogonal spreads
- A new almost perfect nonlinear function which is not quadratic
- Finite semifields and projective planes
- New criteria for MRD and Gabidulin codes and some rank-metric code constructions
- Perfect nonlinear functions and cryptography
- Generalized twisted fields
- Notes on APN functions, semibiplanes and dimensional dual hyperovals
- On quadratic APN functions and dimensional dual hyperovals
- On the nuclei of a finite semifield
- Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes
- Switching Construction of Planar Functions on Finite Fields
- Coding for Errors and Erasures in Random Network Coding
- A Rank-Metric Approach to Error Control in Random Network Coding
