Which discrete math journal should I choose to publish my findings? I have some results, related to imposing group structures on subspaces of finite fields with a metric, and I would like to publish my work. My advisor asked me to choose a journal, but I have no idea how to decide.

I have some further results on a paper published in Linear Algebra and its Applications. I have resolved a few open question they pose in their paper. 

Is it advisable that I publish my results in the same journal? What other options do I have? How do I know if it is a good journal?
One good place to start is the journals in which your most important references were published. (The authors of those references would be good candidates if the journal asks you to propose referees.)

Or: ask other people that work in the same field what journal they would suggest. (While you are at it, send them the manuscript and ask them for comments, nicely.) Have you presented your results at a conference? Do you recall anyone there working on a similar topic? Ideally someone who sat in on your presentation?

Your advisor should have at least a passing acquaintance with your field, so he should be able to suggest something. That he does not do so suggests to me that he is watching how you cope with this situation :-) How about other students of your advisor, does anyone work in this field?

It is not easy to judge whether a given journal is good. @EnergyNumbers' comment is helpful.