Classification of $3\mathrm{mod}5$ arcs in $\mathrm{PG}(3,5)$

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 $(t\mathrm{mod}q)$-arcs as a general framework for extendability results for codes and arcs. Here we complete the known partial classification of $(3\mathrm{mod}5)$-arcs in $\mathrm{PG}(3,5)$ 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.

33 pages, 15 tables; typos corrected

References in corpus (1)

• Computer classification of linear codes

Cited by in corpus (1)

• The Geometry of $(t\mathrm{mod}q)$-arcs