Generalized Hamming weights of additive codes and geometric counterparts

Title data

D'haeseleer, Jozefien ; Kurz, Sascha:
Generalized Hamming weights of additive codes and geometric counterparts.
Bayreuth , 2025 . - 57 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008780

Official URL:

Abstract in another language

We consider the geometric problem of determining the maximum number n_q(r,h,f;s) of (h-1)-spaces in the projective space PG(r-1,q) such that each subspace of codimension f does contain at most $s$ elements. In coding theory terms we are dealing with additive codes that have a large f-th generalized Hamming weight. We also consider the dual problem of the minimum number b_q(r,h,f;s) of (h-1)-spaces in PG(r-1,q) such that each subspace of codimension f contains at least s elements. We fully determine b_2(5,2,2;s) as a function of s. We additionally give bounds and constructions for other parameters.

Further data

Item Type:	Preprint, postprint
Keywords:	additive codes; Galois geometry; blocking sets; subspace codes
Subject classification:	Mathematics Subject Classification Code: 94Bxx (51E22)
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:	20 Dec 2025 22:00
Last Modified:	22 Dec 2025 09:58
URI:	https://eref.uni-bayreuth.de/id/eprint/95503