Construction of New Asymptotic Classes of Binary Sequences Based on Existing Asymptotic Classes

In this paper, we first demonstrate on optimally shifted Legendre sequences that an addition of a ±1 to the front of all binary sequences belonging to that class does not change the asymptotic value of the aperiodic merit factor. We then extend this result to a general case, showing that concatenation of a ±1 to the front of all sequences belonging to any asymptotic class does not affect the asymptotic merit factor value. Additionally, we present a bound on how many bits can be concatenetaded to the front before the asymptotic value becomes affected. Finally, we discuss our attempts to find classes of binary sequences with asymptotic aperiodic merit factor of 7 or greater and present a relationship between the periodic and aperiodic merit factors.