General asymptotic conjecture for the normalized linear complexity of composed arrays

Let $\text{\bf A}$ be an array constructed by composing a shift sequence or array with a column sequence $\text{\bf C}$ or a floor array $\text{\bf F}$ of suitable dimensions. Write ${\cal L}_n(\text{\bf A})$ for the normalized linear complexity of $\text{\bf A}$, and similarly ${\cal L}_n(\text{\bf C})$ and ${\cal L}_n(\text{\bf F})$ for the column and floor, respectively.

General asymptotic conjecture. As the size of $\text{\bf A}$ increases, ${\cal L}_n(\text{\bf A})$ approaches ${\cal L}_n(\text{\bf C})$ or ${\cal L}_n(\text{\bf F})$, according as the construction uses the column sequence or the floor array.

This conjecture generalizes the observed behavior of the constructions considered in the paper: the normalized linear complexity of the composed array approaches that of its constituent column or floor sequence/array. The cited constructions and numerical experiments provide supporting evidence, but no general proof is given.