A new family of MRD-codes
By Bence Csajb'ok, Giuseppe Marino, Olga Polverino, Corrado Zanella. Linear Algebra and its Applications, 2017
103 citations recorded by the source corpus.
We introduce a family of linear sets of $\mathrm{PG}(1,q^{2n})$ arising from maximum scattered linear sets of pseudoregulus type of $\mathrm{PG}(3,q^{n})$. For $n=3,4$ and for certain values of the parameters we show that these linear sets of $\mathrm{PG}(1,q^{2n})$ are maximum scattered and they yield new MRD-codes with parameters $(6,6,q;5)$ for $q>2$ and with parameters $(8,8,q;7)$ for $q$ odd.
Subfields: Artificial Intelligence, Computer Networks and Communications, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/40aa1706dfac47b274bb256c4ff5d7307a18d581
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Citations in the corpus
- New semifields and new MRD codes from skew polynomial rings (2018, background): “Many of the known constructions exploit the correspondence between matrices (or vector space endomorphisms) and linearized polynomials; see, for example, [6, 44].”
- Exceptional scattered polynomials (2017, unknown): “(5) f(x) = δx s + x n/2+s , for n = 6, 8 and some δ ∈ Fqn ; see [11].”