A subspace code of size 333 in the setting of a binary q-analog of the Fano plane

Daniel Heinlein*, Michael Kiermaier, Sascha Kurz, Alfred Wassermann

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum subspace distance 4 and cardinality 333, i.e., 333≤A2(7,4;3), which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in one of 31 conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.

Original languageEnglish
Pages (from-to)457-475
Number of pages19
JournalAdvances in Mathematics of Communications
Volume13
Issue number3
DOIs
Publication statusPublished - Aug 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Finite groups
  • finite projective spaces
  • constant dimension codes
  • subspace codes
  • subspace distance
  • combinatorics
  • computer search
  • AUTOMORPHISM GROUP
  • PROJECTIVE SPACES
  • CONSTRUCTION
  • GEOMETRIES
  • DESIGNS

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