Solving linear systems of determinant frequently zero over finite field GF(2)

Abstract We present a regular algorithm for solving linear systems over the finite field GF (2) from the viewpoint of linear functionals. The algorithm is quite useful for solving a system of linear equations Ax = b of which the determinant of the matrix A is zero. The time complexity of the algorithm is O ( n ). A number of 2 n − 1 processing elements (PEs) connected in a full binary tree are required to accomplish the computations of the algorithm for systems of n equations in n unknowns, and all PEs can be implemented in an m × m (the least square greater than 2 n − 1) array of processors in quite a simple logic.