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Minimal solutions of the isometry equation. (English) Zbl 1395.05033

Summary: For a finite vector space \(W\) over \(\mathbb{F}_q\), there are described all the pairs of multisets \(\{V_1, \dots, V_{q + 1} \}\) and \(\{U_1, \dots, U_{q + 1} \}\) of subspaces in \(W\) such that for all \(w \in W\) the equality \(| \{i \mid w \in V_i \} | = | \{i \mid w \in U_i \} |\) holds.

MSC:

05B40 Combinatorial aspects of packing and covering
94B05 Linear codes (general theory)
15A03 Vector spaces, linear dependence, rank, lineability
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