Contest problems with connections to deeper mathematics

This question is with regard to Elkies' answer to the above post.

Vandermonde determinant can be computed using FFT techniques.

Can Moore determinant(including modulo some integer) be computed using FFT techniques?

Contest problems with connections to deeper mathematics

This question is with regard to Elkies' answer to the above post.

Vandermonde determinant can be computed using FFT techniques.

Can Moore determinant(including modulo some integer) be computed using FFT techniques?

Contest problems with connections to deeper mathematics

This question is with regard to Elkies' answer to the above post.

What is the complexity of computing the determinant of a given $n \times n$ full rank Moore matrix modulo some integer?

Vandermonde determinant can be computed using FFT techniques in $O(n\log^{a}{n})$ for some $a \in \mathbb{R}_{+}$.

Can Moore determinant be likewise reduced from $O(n^{3})$ to $O(n\log^{b}{n})$ for some $b \in \mathbb{R}_{+}$ (if so is there a reference)?

Contest problems with connections to deeper mathematics

This question is with regard to Elkies' answer to the above post.

Vandermonde determinant can be computed using FFT techniques.

Can Moore determinant(including modulo some integer) be computed using FFT techniques?