Abstract
The generalized inverses of systematic non-square binary matrices have
applications in mathematics, channel coding and decoding, navigation
signals, machine learning, data storage and cryptography such as the
McEliece and Niederreiter public-key cryptosystems. A systematic
non-square $(n-k) \times k$ matrix $H$, $n
> k$, has $2^{k\times(n-k)}$
different generalized inverse matrices. This paper presents an algorithm
for generating these matrices and compares it with two well-known
methods, i.e. Gauss-Jordan elimination and Moore-Penrose methods. A
random generalized inverse matrix construction method is given which has
a lower execution time than the Gauss-Jordan elimination and
Moore-Penrose approaches.