McEliece variants that support signatures
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.