ALGORITMO PARA EL CÁLCULO DE LA INVERSA DE UNA MATRIZ EN GLn(Z2)

Abstract

ABSTRACT
In this work we present a new algorithm that allows us, given an invertible matrix with entries in the field Z2
(boolean matrix), obtain its inverse. The algorithm transforms the matrix, written in its classical form, into
polynomials over the binary field Z2, from which the inverse of the matrix is computed. The advantage of this
algorithm is that it allows us to solve linear equations system in the form XA = Y, with known Y and A, where A ∈
GLn (Z2) and Y ∈ (Z2)n, without need of explicitly computing the inverse matrix, but using instead the polynomials,
associated to the matrix A. The algorithm is implemented on Mathematica language (Version 4.0).