Frobenius orbit codes and finite-field Fourier spectra: exact distance and coset distributions

David Kumallagov, Daniil Sizikov, Anton Zarubin

Let $q$ be a prime power, let $m\ge 1$, put $Q=q^m$, and let a permutation $\pi$ of a finite index set $I$ satisfy ${\pi }^m=1$. We study the $\F q$-linear code \[ \mathcal C(π)=\{x\in\Lfi…