Exhaustive search for long low autocorrelation binary codes using length-increment algorithm

Finding binary sequences with low autocorrelation is very important in many applications and their construction is a hard computational problem. Here a new exhaustive search algorithm is developed to find all optimal aperiodic binary sequences which are faster than simple one and it achieves its efficiency through a combination of the following four devices: (1) a branch-and-bound search strategy; (2) search logic that avoids codes redundant relative to two PSL-preserving operations; (3) a fast recursive method for computing autocorrelation functions of binary sequences; (4) a simple scheme for partitioning and parallelizing, made possible by the fixed upper bound on PSL. (4 pages)