The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of importance or noise. From a coding-theoretic perspective, the actual error-correction capability of a code under this metric can exceed half its minimum distance. In this work, we establish direct bounds on this capability, tightening those obtained via minimum-distance arguments. We also propose a flexible code construction based on generalized concatenation and show that these codes can be efficiently decoded up to a lower bound on the error-correction capability.

翻译：加权汉明度量通过对坐标块分配不同权重，推广了汉明度量。它非常适用于诸如在独立并行信道上的编码等应用，其中每个信道具有不同的重要性或噪声水平。从编码理论的角度看，码在此度量下的实际纠错能力可能超过其最小距离的一半。在这项工作中，我们建立了关于此能力的直接界，改进了通过最小距离论证所得的界。我们还提出了一种基于广义级联的灵活码构造，并证明了这些码可以高效地解码至纠错能力的一个下界。