High-Performance Kernels for Exact Linear Algebra

The Grenoble based software libraries LinBox, Fflas/ffpack, and Givaro support exact linear algebra computation.  I will review the state of the art in these and other libraries of kernels (such as matrix multiplication --- GEMM) for matrix arithmetic over finite fields.  In particular, I'll discuss the potential of the BLIS framework to contribute to our tools for these fundamental matrix operations, particularly over tiny fields such as GF2, GF3, GF5, and for symmetric matrix operations.