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

08/10/2021

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by   Sascha Kurz, et al.

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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 (tmod 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.