Additive Subspace Signature I realise there are homomorphic signatures for short messages, for instance with RSA encryption we have a signature scheme where $S(m_1 m_2) = S(m_1)S(m_2)$.

I would like to know if there's a signature scheme where the messages may be linear additive combinations of the basis vectors $(v_1, \dots, v_n)$ and where, if $v$ is in the subspace spanned by the basis vectors $(v_1, \dots, v_m)$ and the signatures $S(v_1), \dots, S(v_m)$ are known, it is possible to construct $S(v)$ from them.
The following papers constructs linearly homomorphic signature schemes. 

Pairing based signatures:


https://eprint.iacr.org/2006/025.pdf
https://crypto.stanford.edu/~dabo/papers/netcode.pdf


Lattice-based signatures:


https://eprint.iacr.org/2010/453.pdf