Direct methods for sparse matrices
Direct methods for sparse matrices
Parallel sparse LU decomposition on a mesh network of transputers
SIAM Journal on Matrix Analysis and Applications
Factoring polynomials over finite fields using differential equations and normal bases
Mathematics of Computation
An acceleration of the Niederreiter factorization algorithm in characteristic 2
Mathematics of Computation
Factorization of polynomials over finite fields and characteristic sequences
Journal of Symbolic Computation
Arithmetic and factorization of polynomial over F2 (extended abstract)
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Modern computer algebra
Factoring high-degree polynomials over f2 with Niederreiter's algorithm on the IBM SP2
Mathematics of Computation
Factoring a binary polynomial of degree over one million
ACM SIGSAM Bulletin
The black-box Niederreiter algorithm and its implementation over the binary field
Mathematics of Computation
Communication-efficient parallel generic pairwise elimination
Future Generation Computer Systems - Special section: Information engineering and enterprise architecture in distributed computing environments
Hi-index | 0.00 |
An important factorization algorithm for polynomials over finite fields was developed by Niederreiter. The factorization problem is reduced to solving a linear system over the finite field in question, and the solutions are used to produce the complete factorization of the polynomial into irreducibles. One charactersistic feature of the linear system arising in the Niederreiter algorithm is the fact that, if the polynomial to be factorized is sparse, then so is the Niederreiter matrix associated with it. In this paper, we investigate the special case of factoring trinomials over the binary field. We develop a new algorithm for solving the linear system using sparse Gaussian elmination with the Markowitz ordering strategy. Implementing the new algorithm to solve the Niederreiter linear system for trinomials over F2 suggests that, the system is not only initially sparse, but also preserves its sparsity throughout the Gaussian elimination phase. When used with other methods for extracting the irreducible factors using a basis for the solution set, the resulting algorithm provides a more memory efficient and sometimes faster sequential alternative for achieving high degree trinomial factorizations over F2.