Bounded cyclic-exchange conjecture for basis sequences

Let $(B_1,\dots,B_k)$ and $(B'_1,\dots,B'_k)$ be compatible sequences of $k$ bases of a rank-$r$ matroid. A cyclic exchange is the simultaneous cyclic transfer of elements among distinct basis positions, with every resulting set required to be a basis. Bounded cyclic-exchange conjecture. The sequence $(B_1,\dots,B_k)$ can be transformed into $(B'_1,\dots,B'_k)$ by using at most $r$ cyclic exchanges. This is proposed as a generalization of Hamidoune's conjecture and is presented as open in the source.