Besides the Niederreiter cryptosystem, are there any other variants that support digital signatures? Can any of them sign arbitrary signatures unlike the Niederreiter cryptosystem? What are the key and signature sizes?
There is a variant of the Neiderreiter system by Courtois, Finiasz, and Sendrier found in their paper: "How to achieve a McEliece-based Digital Signature Scheme" from Asiacrypt 2001. The Wikipedia article on the Neiderreiter Cryptosystem provides a brief introduction to this signature. There is an element of trial and error in the signing process that is cumbersome but it should work for all message hashes.