Title: The M4RIE library for dense linear algebra over small fields with even characteristic
Abstract: We describe algorithms and implementations for linear algebra with dense matrices over F2e for 2 ≤ e ≤ 10. Our main contributions are: (1) a specialisation of precomputation tables to F2e, called Newton-John tables in this work, to avoid scalar multiplications in Gaussian elimination and matrix multiplication, (2) an efficient implementation of Karatsuba-style multiplication for matrices over extension fields of F2 and (3) a description of an open-source library -- called M4RIE -- providing the fastest known implementation of dense linear algebra over F2e with 2 ≤ e ≤ 10.