Sequences with perfect linear complexity profile were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently apwenian sequences, first with values ±1, then with values in $\{0,1\}$, were introduced in the study of Hankel determinants of automatic sequences. We explain that these two families of sequences are the same up to indexing, and give consequences and questions that this implies. We hope that this will help gathering two distinct communities of researchers.

中文翻译：

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完美的线性复杂度曲线和Apwenian序列

二十年前，在研究二进制序列随机性的方法中定义了具有完美线性复杂度分布的序列。最近的apwenian序列，首先具有值±1，然后具有$\{0，\mathrm{1个}\}$在研究自动序列的汉高行列式中引入了。我们解释说，直到索引为止，这两个序列族是相同的，并给出了所暗示的结果和问题。我们希望这将有助于聚集两个不同的研究人员社区。