### 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 language | English |
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Pages (from-to) | 457-475 |

Number of pages | 19 |

Journal | Advances in Mathematics of Communications |

Volume | 13 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 2019 |

MoE publication type | A1 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

## Cite this

Heinlein, D., Kiermaier, M., Kurz, S., & Wassermann, A. (2019). A subspace code of size 333 in the setting of a binary q-analog of the Fano plane.

*Advances in Mathematics of Communications*,*13*(3), 457-475. https://doi.org/10.3934/amc.2019029