Ensembles of optimal binary sequences of length 2²ⁿ

Abstract The problem of constructing ensembles of optimal binary sequences of arbitrary period is of great practical importance and urgency, as the electromagnetic spectrum is becoming increasingly congested. The solution to this problem will allow designers of asynchronous wireless communication systems to overcome this congestion, by using ensembles of sequences tailored to their system requirements. This work aims to develop a systematic method for constructing ensembles of sequences with optimal correlation with arbitrary period. Optimality can be strict, or asymptotic, as the period tends to infinity. The problem is of fundamental importance in information theory, with wide-ranging applications to wireless communications, navigation, radar, digital watermarking, and related fields.