CLASSIFICATION OF (3 mod 5) ARCS IN PG(3, 5)

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.