I'm working on generating de Bruijn sequences using a non-binary LFSR (as described in ). One problem I'm running into is finding all irreducible polynomials which can be then used to parametrise the LFSR to generate different de Bruijn sequences. I found some Python libraries which implement operations on Galois fields but they are mostly incomplete and usually can only verify whether a polynomial is irreducible over a given GF (actually I had a similar problem with finding implementation for q-valued LFSR but I ended up rolling my own). Is brute force, i. e. generating all (monic) polynomials and then checking for irreducibility, the only way?
 Philippakis, Anthony A et al. “Design of Compact, Universal DNA Microarrays for Protein Binding Microarray Experiments.” Journal of Computational Biology 15.7 (2008) : 655–665. Web.