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

TL;DR

This paper introduces an improved heuristic algorithm for computationally searching long skew-symmetric binary sequences with high merit factors, achieving new records for sequences of lengths between 201 and 303.

Contribution

An enhanced stochastic search method for finding long skew-symmetric binary sequences with superior autocorrelation properties and high merit factors.

Findings

Discovered new sequences with merit factor >8.5 for lengths 201-303

Found sequences with merit factor >8 for all odd lengths 201-303

Longest sequence with merit factor >9 is of length 255

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.