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

Title data

Kurz, Sascha ; Landjev, Ivan ; Rousseva, Assia:
Classification of (3 mod 5) arcs in PG(3,5).
Bayreuth , 2021 . - 33 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005712

Official URL: Volltext

Abstract in another language

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.

Further data

Item Type: Preprint, postprint
Keywords: Projective geometries; optimal linear codes; quasidi-divisible arcs; (t mod q)-arcs; Griesmer bound
Subject classification: Mathematics Subject Classification Code: 51E22 (51E21 94B05)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 14 Aug 2021 21:00
Last Modified: 16 Aug 2021 05:25
URI: https://eref.uni-bayreuth.de/id/eprint/66801