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
)
Related URLs
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 |