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. 
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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/

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