We construct codes that allow to exactly recover the support of an unknown sparse vector with almost equal absolute values of all nonzero coordinates given results of linear measurements in the presence of noise with \(\ell_p\)-norm bounded from above. We propose a decoding algorithm with asymptotically minimum complexity.

中文翻译：

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从不准确的线性测量中恢复稀疏向量的精确支持的代码及其解码

我们构建的代码允许精确地恢复未知稀疏向量的支持，其中所有非零坐标的绝对值几乎相等，给定存在噪声的线性测量结果，并以 \(\ell_p\) -范数为界。我们提出了一种具有渐进最小复杂度的解码算法。