Geodesic
On the multidimensional permanent and $q$-ary designs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 451-456

Voir la notice de l'article provenant de la source Math-Net.Ru

An $H(n,q,w,t)$ design is a collection of some $(n-w)$-faces of the hypercube $Q^n_q$ that perfectly pierce all $(n-t)$-faces $(n\geq w>t)$. An $A(n,q,w,t)$ design is a collection of some $(n-t)$-faces of $Q^n_q$ that perfectly cover all $(n-w)$-faces. The numbers of H-designs and A-designs are expressed in terms of the multidimensional permanent. Several constructions of H-designs and A-designs are given and the existence of $H(2^{t+1},s2^t,2^{t+1}-1,2^{t+1}-2)$ designs is proven for all $s,t\geq 1$.
Keywords: Steiner system, H-design, perfect matching, clique matching
Mots-clés : MDS code, permanent. 
@article{SEMR_2014_11_a50,
     author = {V. N. Potapov},
     title = {On the multidimensional permanent and $q$-ary designs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {451--456},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a50/}
}
TY  - JOUR
AU  - V. N. Potapov
TI  - On the multidimensional permanent and $q$-ary designs
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2014
SP  - 451
EP  - 456
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a50/
LA  - ru
ID  - SEMR_2014_11_a50
ER  - 
%0 Journal Article
%A V. N. Potapov
%T On the multidimensional permanent and $q$-ary designs
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2014
%P 451-456
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2014_11_a50/
%G ru
%F SEMR_2014_11_a50
V. N. Potapov. On the multidimensional permanent and $q$-ary designs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 451-456. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a50/