I have been paid to develop a piece of code which is being used in a scientific paper. The code is an important piece of this paper, since the paper is about a specific (novel) computational method.
Would it be fair to be included in the list of authors even if I have been paid for it?
If you developed bespoke software for a particular project, it would not be unreasonable to include you as an author. If the software you have developed is more general, you clearly can't expect to be an author on each paper resulting from its use. Whether you are getting paid or not is irrelevant.
Whether you really should be included, or whether it is a bit of a grey area, depends on how much intellectual contribution went into the software. If you took a precisely defined algorithm and done a straight-forward implementation of it, I can't find much fault in denying you authorship. If developing the software included coming up with some details of the algorithm, I'd say you definitely should be an author.
In the comments, Lodinn mentions the CRedit guidelines, which explicitly include a "Software" category for author contributions.
The question you specifically ask relates to fairness, which calls for a rather subjective response. In my view it would be fair for you to be included among the authors, but I also know that some research teams would be more inclined to list your name in the acknowledgements than to put your name in lights along with theirs! On the issue of fairness, I think that the best you can do is argue your case with the other authors.
There are, however, two other issues that are distinct both from each other, and from the issue of fairness. The first is the matter of so-called moral rights; the second relates to the policies of different journal publishers. In those jurisdictions that recognize moral rights, perhaps the foremost right is the to be attributed as the author of a work. For example, in Australia, moral rights (generally) are granted under Part IX of the Copyright Act 1968, and the right of attribution is granted under s. 193. However, it is not all as simple as might first appear. In your particular case, for example, your moral right to be attributed as the author of the software would not arise merely as a consequence of the software being discussed in the paper. Instead, your moral right of attribution would come into play only if the software itself were being published or distributed. In that case, under Australian law, you would be entitled to require that you be named as the author of the software, even though you had been paid for your work, and even though you no longer owned the copyright to the software.
In addition to the matter of moral rights, there is also the question of the policies of different journals. Most publishers require that anyone who makes a substantial contribution to a paper be included in the list of authors but yet again, it is never as simple as first appears. Some journals will view the development of an important piece of software as fulfilling the criteria for a substantial contribution, others will not.
It is worth mentioning that statistical consultants often find themselves in a similar position to yours. Much of the work that statisticians do is viewed by some researchers as "mere technical assistance"; other researchers will recognize it as having been essential to turn data into useful conclusions.
Let's say I read this paper, and the code. After reading everything published, what is my impression? Do I think the authors of the paper wrote the code? Do I think Andrea wrote the code? Do I think the authors of the paper hired someone to write the code for them, or found some publicly available code?
In the first case, if a reader believes falsely that the authors wrote the code, then we have a case of plagiarism, which is a serious problem for the authors. Everything else: You invested your work, and you want something out of it. I do that kind of work purely for the money. Pay me, and I'm fine. You may have done this work to improve your reputation. That's something that needs to be agreed upon beforehand, because you likely traded money for the hope of reputation. I wouldn't necessarily recognise you as a co-author, but definitely add something like "Software designed and created by Andrea".
BTW. In many countries there is a "right of authorship", which means if you wrote it, then you and nobody else has the right to say "I wrote it". That right cannot be sold. The copyright allows them to distribute your code and charge money for it if someone is willing to pay. It doesn't change the fact that you wrote it.
