Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this letter, 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.

中文翻译：

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关于具有破纪录的 PSL 值的长二进制序列的生成

二进制序列广泛应用于各种实际领域，如电信、雷达技术、导航、密码学、测量科学、生物学或工业。在这封信中，提出了一种生成具有低峰值旁瓣电平 (PSL) 值的长二进制序列 (LBS) 的方法。有一个有长度的 LBS$n$，所提出算法的时间和内存复杂度均为 $\mathcal {O}(n)$. 在我们的实验中，我们反复达到比目前已知的现有技术结构更好的 PSL 值，例如带或不带旋转的勒让德序列、带或不带旋转的 Rudin-Shapiro 序列或 m 序列，始终达到破纪录的PSL 值严格小于$\sqrt{n}$. 此外，所提出方法的效率和简单性特别有利于实现的轻量级，这使我们能够在不到一秒的时间内达到破纪录的 PSL 值。