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An automorphism group of an incidence structure I induces a tacticaldecomposition on I. It is well known that tactical decompositions of t-designssatisfy certain necessary conditions which can be expressed as equations interms of the coefficients of tactical decomposition matrices. In this articlewe present results obtained for tactical decompositions of q-analogs oft-designs, more precisely, of 2-(v,k,lambda_2;q) designs. We show thatcoefficients of tactical decomposition matrices of a design over finite fieldsatisfy an equation system analog to the one known for block designs.Furthermore, taking into consideration specific properties of designs over thebinary field, we obtain an additional system of inequations for thesecoefficients in that case.

Tactical decompositions of designs over finite fields