Geodesic
On the most weight \(w\) vectors in a dimension \(k\) binary code
The electronic journal of combinatorics, Tome 17 (2010)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Ahlswede, Aydinian, and Khachatrian posed the following problem: what is the maximum number of Hamming weight $w$ vectors in a $k$-dimensional subspace of $\mathbb{F}_2^n$? The answer to this question could be relevant to coding theory, since it sheds light on the weight distributions of binary linear codes. We give some partial results. We also provide a conjecture for the complete solution when $w$ is odd as well as for the case $k \geq 2w$ and $w$ even. One tool used to study this problem is a linear map that decreases the weight of nonzero vectors by a constant. We characterize such maps.
DOI : 10.37236/414
Classification : 05D05, 05E99, 94B05
Mots-clés : hamming weight vectors, subspace, binary linear codes 
@article{10_37236_414,
     author = {Joshua Brown Kramer},
     title = {On the most weight \(w\) vectors in a dimension \(k\) binary code},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/414},
     zbl = {1204.05096},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/414/}
}
TY  - JOUR
AU  - Joshua Brown Kramer
TI  - On the most weight \(w\) vectors in a dimension \(k\) binary code
JO  - The electronic journal of combinatorics
PY  - 2010
VL  - 17
UR  - http://geodesic.mathdoc.fr/articles/10.37236/414/
DO  - 10.37236/414
ID  - 10_37236_414
ER  - 
%0 Journal Article
%A Joshua Brown Kramer
%T On the most weight \(w\) vectors in a dimension \(k\) binary code
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/414/
%R 10.37236/414
%F 10_37236_414
Joshua Brown Kramer. On the most weight \(w\) vectors in a dimension \(k\) binary code. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/414

Cité par Sources :