publishing an article which contains abstract math and programming on arxiv or journal I have a soft question. I currently study abstract math which includes group theory. On the other hand, I have strong background in c++, data structures etc. So, most of the time I end up with an algorithm or a computer code which mimics or implements a specific problem in group theory. 
I am pretty sure that for the specific groups I am working on, these algorithms(and maybe nested data structures) have not been published or known. Also, sometimes  I see papers which uses gap. So, my question is :
Can I publish these c++ codes somehow? What is the criteria to publish an algorithm which doesn't solve an open problem but helps people understand the problem? Can you provide me essays or examples about this topic? 
Thank you very much.   

There has been a lot of work in Computational group theory. You should definitely check the literature. Anyway, having a real program is fine, but the real contribution are in algorithms. So you can publish a paper describing an algorithm, but you should publish the code elsewhere, e.g., in the web.
