Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z

Abstract

Orthogonal Sequences (as M-Sequences, Walsh Sequences, …) 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 a correct form, especially in the pilot channels, the Sync channels, and the Traffic channel. This research is useful to generate new sets of orthogonal sequences (with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication) from quotient rings Z/pmZ, where Z is the integers and p is prime, replacing each event number by zero and replacing each odd number by one.