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

Titelangaben

Kurz, Sascha ; Landjev, Ivan ; Rousseva, Assia:
Classification of (3 mod 5) arcs in PG(3,5).
In: Advances in Mathematics of Communications. Bd. 17 (2023) Heft 1 . - S. 172-206.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2021066

Volltext

Link zum Volltext (externe URL):

Abstract

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.