Research article of American Journal of Computer Sciences and Applications
Generalization of Hadamard Matrices
Dr. Ahmad Hamza Al Cheikha
Dep. of Mathematical Science, College of Arts-science and Education Ahlia Uni., Manama, Bahrain
Hadamard’s matrices are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in correct form, specially in the pilot channels, the Sync channels, the traffic channel and so much applications in the fields; Modern communication and telecommunication systems, signal processing, optical multiplexing, error correction coding, and design and analysis of statistics.
This research is useful to generate new sets of orthogonal matrices by generalization Hadamard matrices,with getting bigger lengths and bigger minimum distance by using binary representation of the matrices that assists to increase secrecy of these information, increase the possibility of correcting mistakes resulting in the channels of communication, giving idea to construct new coders and decoders by mod p with more complexity for using these matrices and derivation new orthogonal codes or sequences.
Keywords: Hadamard matrix, Binary vector, Coefficient of Correlation, Walsh’s Sequences, Orthogonal sequences, Kronecker product, Code