MRD-codes arising from the trinomial xq+xq3 +cxq5 ∈Fq6 [x]

Giuseppe Marino, Maria Montanucci*, Ferdinando Zullo

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In [10], the existence of Fq-linear MRD-codes of Fq 6×6, with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq6 , defined by a trinomial of Fq6 [x], when q is odd and q≡0,±1(mod5), has been proved. In this paper we show that this family produces Fq-linear MRD-codes of Fq 6×6, with the same properties, also in the remaining q odd cases, but not in the q even case. These MRD-codes are not equivalent to the previously known MRD-codes. We also prove that the corresponding maximum scattered Fq-linear sets of PG(1,q6) are not PΓL(2,q6)-equivalent to any previously known linear set.

Original languageEnglish
JournalLinear Algebra and Its Applications
Volume591
Pages (from-to)99-114
ISSN0024-3795
DOIs
Publication statusPublished - 15 Apr 2020

Keywords

  • Linear set
  • MRD-code
  • Scattered subspace

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