Generalized Hamming weights of additive codes and geometric counterparts

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D'haeseleer, Jozefien ; Kurz, Sascha:
Generalized Hamming weights of additive codes and geometric counterparts.
Bayreuth , 2025 . - 57 S.

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Abstract

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.