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 theĀ 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.
Continue reading “When does the Discrete Fourier Transform Matrix have Nonsingular Submatrices?”