  Binary sequences are widely used in various practical fields, such as
telecommunications, radar technology, navigation, cryptography, measurement
sciences, biology or industry. In this paper, a method to generate long binary
sequences (LBS) with low peak sidelobe level (PSL) value is proposed. Having an
LBS with length $n$, both the time and memory complexities of the proposed
algorithm are $\mathcal{O}(n)$. During our experiments, we repeatedly reach
better PSL values than the currently known state of art constructions, such as
Legendre sequences, with or without rotations, Rudin-Shapiro sequences or
m-sequences, with or without rotations, by always reaching a record-breaking
PSL values strictly less than $\sqrt{n}$. Furthermore, the efficiency and
simplicity of the proposed method are particularly beneficial to the
lightweightness of the implementation, which allowed us to reach
record-breaking PSL values for less than a second.
