I committed support for finite fields up to degree 16 to M4RIE a few days ago. Furthermore, the dependency on Givaro for constructing finite fields was dropped.
Don’t get me wrong. Givaro is a fine library, much better than what I wrote for M4RIE. However, it is a C++ library while M4RIE is a C library and the little functionality of finite field arithmetic needed in M4RIE was not that hard to add natively. In the past M4RIE relied on Givaro for running tests and benchmarks, the core library was always free of C++. However, as we plan to add support for high-degree polynomials over matrices over, we need the ability to create finite extensions of on the fly in the core library.