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Partial results on the possible effective lengths of divisible codes

Title data

Körner, Theresa ; Kurz, Sascha:
Partial results on the possible effective lengths of divisible codes.
2023
Event: Workshop Combinatorics in Digital Communication , 19.-21.04.2023 , Eindhoven, Netherlands.
(Conference item: Workshop , Speech )

Abstract in another language

A linear code C over GF(q) is called ∆-divisible if the Hamming weights wt(c) of all codewords care divisible by ∆. Divisible codes were first studied by Harold Ward.
When we associate each subspace U in PG(n−1,q) with its characteristic function that maps each point
to an non-negative integer multiplicity
we get a connection between divisible codes and Galois geometries. A mapping from the pointset of
PG(n − 1, q) to the integers is called ∆-divisible if the corresponding linear code associated with the multiset of
points is ∆-divisible.

There exist some upper bounds for partial spreadsusing that the corresponding divisible codes must be projective. For the characterization result for the possible (effective) lengths of q^r-divisible codes quite large point multiplicities are needed on the constructive side, so there is a requirement for more refined results on different parameters e.g. the maximum possible point multiplicities
or the dimension. In this talk I present some partial results on the possible effective lengths of divisible
codes with extra constraints.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Theresa Körner
Keywords: divisible codes; linear codes; partial spreads; Galois Geometry; Subspace Codes
Subject classification: Mathematics Subject Classification Code: 94B05 (51E23)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 26 Apr 2023 08:16
Last Modified: 26 Apr 2023 08:16
URI: https://eref.uni-bayreuth.de/id/eprint/76103