Partial results on the possible effective lengths of divisible codes

Titelangaben

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

Weitere URLs

Abstract

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.