I want to code a solver for nonsingular systems of $N$ linear equations in $N$ unknowns (say up to $N=100$) with an asymmetric Toeplitz matrix. I know that the Levinson algorithm can solve it in time $O(N^2)$ and I am looking for a solution with this complexity. I have seen mentions of alternative approaches such as Schur decomposition, LDU decomposition, Bareiss, Cholesky...
The equations are established in a Galois field, so that stability is not at all an issue here.
I am seeking advice for a good method to implement. My priorities are
ease of implementation,
low memory requirements.
I am not specially looking for superfast methods ($o(N^2)$), unless they are appropriate for moderate $N$, and simple.
What do you recommend?