A Generalization of Some Special Type of Product of Matrices

Pages:68-70
Monika Sangwan (Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Haryana)

Matrices generator matrices and parity check matrices – are the tools in construction and study of error correcting codes. Also whilec codes of smaller lengths with desired correction capabilities can be easily developed, developing large codes presents serious difficulties, with codes becoming in-efficient. A practical way to obtain large codes is to obtain them by some laws of composition over those of shorter length. Kronecker product has been found an effective way of getting larger codes with elegant minimum distance properties from two component codes. However, while the minimum distance of the product code is product of the minimum distances of the component codes, the redundant digits also get multiplied. The paper considers a very general way of product of matrices, which generalizes Kronecker product of matrices. Starting from this generalization of product of matrices, a special type of product, called ‘Rank Partitioned Product’ (RPP) of matrices is defined.