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To the theory of $q$-ary Steiner and other-type trades | | Denis Krotov
; Ivan Mogilnykh
; Vladimir Potapov
; | | Date: |
11 Dec 2014 | | Abstract: | We introduce the concept of a clique bitrade, which generalizes several known
types of bitrades, including latin bitrades, Steiner $T(k-1,k,v)$ bitrades,
extended $1$-perfect bitrades. For a distance-transitive graph $G$, we show a
one-to-one correspondence between the clique bitrades that meet the
weight-distribution lower bound on the cardinality and the bipartite isometric
subgraphs that are distance-regular with certain parameters. As an application
of the results, we find the minimal cardinality of $q$-ary Steiner
$T_q(k-1,k,v)$ bitrades and show a connection of such bitrades with dual polar
subgraphs of the Grassmann graph $J_q(v,k)$. Keywords: trades, bitrades,
Steiner system, $q$-ary designs | | Source: | arXiv, 1412.3792 | | Services: | Forum | Review | PDF | Favorites | |
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