Discovering and analyzing binary codes based on monocyclic quasi-orthogonal matrices

Abstract

New noise-immune codes as an alternative to Barker codes are searched for and studied. The construction of the codes is based on using the features of quasi-orthogonal matrices, including special Mersenne and Raghavarao matrices with cyclic structure. It has been demonstrated that these new codes exceed Barker codes, which are known to be the only codes with the highest peak side lobe ratio (PSLR). Their autocorrelation functions are compared in this work. The usage of the new codes obtained from rows of quasi-orthogonal Mersenne matrices is meant to increase the characteristics of compression, detection, accuracy, resolution, and noise immunity. The results obtained are meant to be used in modern radar, telecommunication, ultra-wideband, and “intellectual” systems of data detection and transmission.