Identifiers for MRD-codes

Abstract

For any admissible value of the parameters $n$ and $k$ there exist $[n,k]$-Maximum Rank distance ${\mathbb{F}}_q$-linear codes. Indeed, it can be shown that if field extensions large enough are considered, almost all rank distance codes are MRD. On the other hand, very few families up to equivalence of such codes are currently known. In the present paper we study some invariants of MRD codes and evaluate their value for the known families, providing a new characterization of generalized twisted Gabidulin codes.

23 pages/post-print version

References in corpus (7)

• Generalized Twisted Gabidulin Codes
• On kernels and nuclei of rank metric codes
• Algebraic structures of MRD Codes
• A characterization of linearized polynomials with maximum kernel
• New Criteria for MRD and Gabidulin Codes and some Rank-Metric Code Constructions
• A Characterization of the Number of Roots of Linearized and Projective Polynomials in the Field of Coefficients
• A new family of MRD codes in ${\mathbb{F}}_q^{2n\times 2n}$ with right and middle nuclei ${\mathbb{F}}_{q^n}$

Cited by in corpus (7)

• Vertex properties of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$
• Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants
• A new family of maximum scattered linear sets in $\mathrm{PG}(1,q^6)$
• MRD-codes arising from the trinomial $x^q+x^{q^3}+c{x}^{q^5}\in {\mathbb{F}}_{q^6}[x]$
• Connections between scattered linear sets and MRD-codes
• On certain linearized polynomials with high degree and kernel of small dimension
• A geometric invariant of linear rank-metric codes