[...] I suppose you would have to give the step matrix below the character in the character list,
Yes, you have to give it somewhere in the paper.
although that sounds different from any character list I have ever seen (I never saw any character list with step-matrices).
Here's an example. http://dpc.uba.uva.nl/ctz/vol77/nr03/art02
(Hidden somewhere in the enormous Appendix 1.)