engleski

Searching for designs over finite fields with non- trivial automorphism groups

A design over the finite field F_q with parameters t-(v, k, lambda)_q is a pair (V, B) where V is the v-dimensional vector space over F_q and B is a collection of k-dimensional subspaces of V, such that each t-dimensional subspace of V is contained in precisely lambda members of B. We follow the trend of finding q- analogues of statements valid for classical combinatorial designs. In particular, we focus on necessary conditions on the existence of designs over finite fields with an assumed automorphism group. We give insight into the problems we encountered as well as results we obtained.

design over finite field ; q-analog of design ; automorphism group ; tactical decomposition

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