Computational Search of Long Skew-symmetric Binary Sequences with High Merit Factors

Abstract

In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult optimization problem. An improved version of the heuristic algorithm is presented and tackled to search for aperiodic binary sequences with good autocorrelation properties. High-performance computations with the execution of our stochastic algorithm to search skew-symmetric binary sequences with high merit factors. After experimental work, as results, we present new binary sequences with odd lengths between 201 and 303 that are skew-symmetric and have the merit factor F greater than 8.5. Moreover, an example of a binary sequence having F > 8 has been found for all odd lengths between 201 and 303. The longest binary sequence with F > 9 found to date is of length 255.

Keywords

• Golay's merit factor, binary sequences, aperiodic autocorrelation sidelobes, skew symmetry