### Abstract

Let (Formula presented.) denote the maximum cardinality of a set (Formula presented.) of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, (Formula presented.), such that any two different subspaces (Formula presented.) have a distance (Formula presented.) of at least d. Lower bounds on (Formula presented.) can be obtained by explicitly constructing corresponding sets (Formula presented.). When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of (Formula presented.). With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on (Formula presented.) and (Formula presented.) for 8 ⩽ n ⩽ 11 are obtained.

Original language | English |
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Pages (from-to) | 179-183 |

Number of pages | 5 |

Journal | Experimental Mathematics |

Volume | 27 |

Issue number | 2 |

Early online date | 31 Oct 2016 |

DOIs | |

Publication status | Published - 2018 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- constant-dimension codes
- integer linear programming
- packing
- random network coding

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## Cite this

*Experimental Mathematics*,

*27*(2), 179-183. https://doi.org/10.1080/10586458.2016.1239145