Classification of $ \mathbf{(3 \!\mod 5)} $ arcs in $ \mathbf{ \operatorname{PG}(3,5)} $
Sascha Kurz, Mathematisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany, Ivan Landjev, Assia Rousseva · Advances in Mathematics of Communications · 2021
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 $ \operatorname{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.