We present new efficient recursive decoders for the Barnes-Wall lattices based on their squaring construction. The analysis of the new decoders reveals a quasi-quadratic complexity in the lattice dimension and a quasi-linear complexity in the list-size. The error rate is shown to be close to the universal lower bound in dimensions 64 and 128.

中文翻译：

---

关于 Barnes-Wall 格的解码

我们基于 Barnes-Wall 格的平方构造提出了新的高效递归解码器。新解码器的分析揭示了格维的准二次复杂度和列表大小的准线性复杂度。错误率显示为接近维度 64 和 128 的通用下限。