## Title data

Kurz, Sascha ; Landjev, Ivan ; Rousseva, Assia:

**Classification of (3 mod 5) arcs in PG(3,5).**

*In:* Advances in Mathematics of Communications.
Vol. 17
(2023)
Issue 1
.
- pp. 172-206.

ISSN 1930-5346

DOI: https://doi.org/10.3934/amc.2021066

## Abstract in another language

The proof of the non-existence of Griesmer [104,4,82]_5-codes is just one of many examples where extendability results are used. In a series of papers Landjev and Rousseva have introduced the concept of (t mod q)-arcs as a general framework for extendability results for codes and arcs. Here we complete the known partial classification of (3 mod 5)-arcs in PG(3,5) and uncover two missing, rather exceptional, examples disproving a conjecture of Landjev and Rousseva. As also the original non-existence proof of Griesmer [104,4,82]_5-codes is affected, we present an extended proof to fill this gap.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Projective geometries; optimal linear codes; quasidi-divisible arcs; (t mod q)-arcs; Griesmer bound |

Subject classification: | Mathematics Subject Classification Code: 51E22 (51E21 94B05) |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 22 Dec 2022 06:25 |

Last Modified: | 22 Dec 2022 06:25 |

URI: | https://eref.uni-bayreuth.de/id/eprint/73183 |