Abstract In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect.

中文翻译：

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使用有限域中的分圆类构造伪随机二元格

摘要 2006 年，Hubert、Mauduit 和 Sárközy 将二元序列的概念扩展到 n 维二元格，并引入了二元格的伪随机性度量。2011 年，Gyarmati、Mauduit 和 Sárközy 将族复杂性、碰撞和雪崩效应的概念从二元序列扩展到二元格。在本文中，我们利用有限域中的分圆类构造伪随机二元格，研究k阶伪随机测度、族复杂度、碰撞和雪崩效应。结果表明，这种二元格是“好”的，并且它们的族在族复杂性、碰撞和雪崩效应方面具有良好的结构。