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Weighted-Hamming Metric: Bounds and Codes
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Weighted-Hamming Metric: Bounds and Codes
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Paper
Weighted-Hamming Metric: Bounds and Codes
2026
Overview
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.
Publisher
Cornell University Library, arXiv.org
Subject
