I am studying a coding theory problem. The question is this:
Open Question: Is there a prime and a positive integer such that all submatrices of the Discrete Fourier Transform matrix over the field are nonsingular?
Currently, I have only counterexamples: Let be the degree of the smallest extension over which contains a nontrivial th root of unity. Then, I know a lot of primes for which the matrix has a singular submatrix.
In this post, I am going to show a failed attempt to answer this question using the results in this paper by Evra, Kowalski, and Lubotzky.