The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
The Design of Rijndael
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Algorithm 898: Efficient multiplication of dense matrices over GF(2)
ACM Transactions on Mathematical Software (TOMS)
Faster multiplication in GF(2)[x]
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Parallel Gaussian elimination for Gröbner bases computations in finite fields
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Simultaneous modular reduction and Kronecker substitution for small finite fields
Journal of Symbolic Computation
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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.